To start with, the thing most often said of Nicolas Cage: he is weird-looking, with constituent parts that don't promise to add up to a movie star. His hair, like cultivated grassland, is lush at the top and sparse at the root. There is something puppety about his face. And, of course, there are his eyes, which, like the Woody Allen joke – "You have the most eyes I've ever seen on any person" – qualify him to play both romantic leads and psychopaths. At 49, Cage overturns every industry standard, and there's no denying it: the result is transfixing. "Have a blueberry muffin," he says in that agonised drawl, and flashes a goofy grin.

We are in a hotel in Mobile, Alabama, a small town on the Gulf Coast where he and Danny Glover are filming an action movie called Tokarev, in which Cage plays a reformed mobster reluctantly returning to his violent roots when his daughter is kidnapped. (The day before, they filmed a car chase down the main street and the excitement still ripples through the glutinous air.) It sounds like a classic Cage role, not that he allows for the existence of such a thing. Cage is methodical in rebutting preconceived notions about himself. "There is a misperception, if you will, in critical response or even in Hollywood, that I can only do exaggerated characters. Or what they would call over-the-top performances." He pauses, as if issuing an historic statement from the podium: "Well, this is completely false."

And: "Another misconception about me is that I just do movies for pay cheques."

And: "That I'm obsessed with comics."

And: "The other big misconception, which needs to be cleared up in my opinion, is video on demand." (His new movie, The Frozen Ground, has a limited cinema release and will be available on demand, which, given the demand for on demand, Cage wishes critics would stop using as shorthand for failure.)

Also, his reputation for excess. "For a while there, it was the three Cs; castles, comic books and cars." He gives me a doleful look. "I just can't get that stuff off of me."

It's true, Cage has always been difficult to place, moving between genres, styles and accents more than most actors in his league. Even his dress, today, is contradictory, the pastel polo shirt at odds with the tattoos and big jewellery – part country club, part rocker. It is also safe to say that his talent for grotesques is largely what made him. More than one director has threatened to fire Cage for going overboard. In 1987, Norman Jewison told him to quit trying to play Ronny, in Moonstruck, with art house surrealism. His uncle, Francis Ford Coppola, nearly fired him for the falsetto he insisted on using for the role of Charlie in Peggy Sue Got Married. Not everything he does turns on high volume. He plays defeat very well, too – it's in the stoop of his shoulders, the slump at the back of his neck – and there is what the US film critic Roger Ebert famously called Cage's "inner tremble", that look of excruciated bafflement that speaks to the panic of being alive.

In different circumstances, Cage might have been a character actor in the style of Steve Buscemi. But there is a grandness to him that demands centre stage. He would make a terrific Richard III, if he didn't believe Americans can't do Shakespeare ("I just don't think we get it. We don't get it right"). I don't know many actors who can make the statements he does and get away with them. To wit, on the subject of the Guardian's recent NSA revelations: "I am paraphrasing Benjamin Franklin, one of my founding fathers, who said something to the effect that, 'Those that would give up their liberty for a little bit of security deserve neither.' And then I'll quote myself: 'The truth is always crucified.' End quote." His tone is so dry that everything he says comes out tinged with self-mockery.

Cage's three most baroque roles have been as the dying, grandiose drunk in Leaving Las Vegas; the coke-addled cop in Werner Herzog's Bad Lieutenant; and, most memorably perhaps, the deranged creep in Vampire's Kiss, in some ways the quintessential Cage movie and the main source of scenes for the internet montage Nicolas Cage Losing His s***, in which, at one stage, Cage is literally chewing the scenery. "Oh my god. I just can't keep up with that stuff," he says. "The internet has developed this thing about me – and I'm not even a computer guy, you know? I don't know why it is happening. I'm trying not to… lemme say this: I'm now of the mindset that, when in Rome, if you can't beat 'em, join 'em."

Most of it seems affectionate, I suggest.

"Well," a sudden, sardonic smile, "it is, but with enormous amounts of irony. Affection loaded with irony."

It doesn't bother him, overly. What bothers him these days is – brace yourselves – craft. "I'm at this point where I don't want to act. It's not about putting things on, it's about taking things off. And trying to be as naked as I can be as a film presence."

Music, he has decided, is "the highest art form", and to this end the only hero he has right now is Anthony Hopkins, who he recently discovered "is a marvellous, magnificent classical composer. I was always such a huge fan of him as an actor; now I can see it in his acting, the way he delivers his dialogue, it's musical. Even in Thor, when the young upstart says, 'I'm king', and Hopkins says [cue booming Sir Tony impression], 'You're NOT; KING; YET.' " Cage strikes a theatrical pose. "It's music! Ba-BA; BA; BA."

He comes from the non-acting branch of the Coppola family: his father August (brother of Francis) is a comparative literature professor and his mother, Joy, a former dancer. Although Cage's manner is courtly in what seems like the southern style, he comes from Long Beach, California, and went to Beverly Hills High. He grew up, he says, in "modest circumstances. Extremely modest. My father was living on a teacher's salary. He took a path that doesn't always lead to fame and fortune, but that was his passion."

Was he the black sheep? "How do I say this in a way that there's diplomacy, because we're talking about a very famous family…"

Oh, please, we're not talking about the Medicis.

"The point is, my father stuck to his guns and he was interested in literature. And he was also an outstanding educator." Cage calls his father his biggest career influence for exposing him to films that would, years later, inform his style as an actor.

"Some of it was downright terrifying. But it still got into my consciousness and came back in my work as I developed into a man. I mean, I was watching movies like The Cabinet Of Dr Caligari, and Nosferatu and Fellini's Juliet Of The Spirits when I was five years old. He had this little projector and he'd play it in the house and we'd all watch, and I'd have nightmares. Just nightmares. But then I grew to love it. I said, OK, can I do that today? If you look at Vampire's Kiss, it's all about that memory of Nosferatu; that Germanic, expressionistic acting style."

Vampire's Kiss, in which Cage plays a literary agent labouring under the delusion he is a vampire, is a weird film that is kind of great in its weirdness and in which Cage exposes himself fearlessly to ridicule, not least for appearing in a horror movie in the first place.

His father wasn't a snob in these matters, nor in the larger matter of his son's desire to be an actor. He didn't pressure him to stay on at school or go to college. Cage (who changed his name from Coppola early on, to see off accusations of nepotism), auditioned for a role in his high school production of West Side Story and, when he didn't get it, opted to leave. "And my father said, it's OK. He told me he was very frustrated with the academic world and you'll probably do better if you go out and try to make it as an actor. And he was right."

His parents had divorced when he was 12 and his mother spent periods in hospital with severe depression, which, Cage says, affected him less than it might have. "I think I was just… some people would call it under the protection of a guardian angel; other people would call it a child's solipsism. It's whatever you want to call it, but I was happy in the bubble of my imagination."

These days, his mother takes great pride in his success. "Yes, she's fun. She watches my movies when they come on television and gets excited. Quite childlike about it, actually." And she stakes a claim in his talent not taken by the Coppolas. "I never studied dance," he says, "but if you look at Wild At Heart, my mother saw that movie and said, 'You are a dancer. Look at how you're moving: all that strange energy is like modern dance.' "

To hear him describe it, Cage's own moods only exist to service his work. Being happy or sad is not the point, he says, with magnificent grandeur: "I invite the entire spectrum, shall we call it, of feeling. Because that is my greatest resource as a film actor. I need to be able to feel everything, which is why I refuse to go on any kind of medication. Not that I need to! But my point is, I wouldn't even explore that, because it would get in the way of my instrument. Which is my emotional facility to be able to perform."

He is aided in this by a solid home life – his wife, Alice, and their seven-year-old son, Kal-El. (He has a grown-up son from a previous relationship.) As a young man, Cage says ruefully, he scorned the idea of stability. "I was a punk rocker, I was rebelling, I didn't want any kind of comfort at home." Being married to Lisa Marie Presley for 108 days, as he was in 2002, fixed that. It's the thing – along with buying and losing all those houses in Europe – that makes people think Cage is nuts. He is an Elvis fan, and one imagines he gravitated towards Lisa Marie for what, in that context, was her superior celebrity.

Cage looks rather surprised. "I was the lesser celebrity? Well, celebrity is a word I take great umbrage with. I'm actively anti-celebrity. I'm about creative expression. That particular relationship was really based on humour. We had a lot of laughs together. So that's what that was. Much was made about it because of her father and whatnot, but we had a simple relationship in my opinion. That was a different time in my life. Many lifetimes ago."

Things are simpler since he shed all those properties, he says. Cage once owned a portfolio including castles in Germany and England, mansions in New Orleans and Rhode Island, and an island in the Bahamas. From the outside, it looks as though he went through a period of testosterone-fuelled property acquisition. Why was that?

"I had to put the money somewhere, and I was a big believer in real estate, and I got caught up in that bubble that exploded. I thought it was real. I didn't trust stocks and I didn't trust just leaving it in the bank. I believed in real estate. So now I'm working through all that."

The properties were sold, mostly at a loss, and he now lives more modestly. "I have a tiny – and I do mean tiny – little cottage in Somerset, near Glastonbury. And I enjoy it that way. The magic of the green hills and the trees and the history. Then I have this other small lifestyle in Las Vegas. Which is a different kind of magic. That's the razzle-dazzle of the city. My wife loves it and we have good friends there. And that's it. That's my life, which is simple. And I want to keep it that way."

He gets upset when people accuse him of saying yes to any job just to pay off his debts, or the jibe that he works too much. "I'm one of those Americans who believes in working. If you've made mistakes in the past, you don't just roll over on people or cave in, you find a way through it. But in film acting, for some reason you get criticised for working."

I'm reminded of something Sean Penn said about him, based on his prolific and populist output: "He's not an actor, he's a performer."

"In a way I agree with him," Cage says. "I would rather be a performer than an actor. Acting to me implies lying. 'He's the greatest actor in the world' is like saying, 'He's the greatest liar in the world.' To perform, in my opinion, is more about emotion."

Penn wasn't being nice, though.

"Well, who knows with him? But that's OK."

Anyway, Cage says, his life these days is extremely stable thanks to Alice. "I made a very clear decision to marry out of my own zip code. I mean, way out of my own zip code. I married into another culture, and it's interesting because in Korea they call me the Son-in-Law."

Alice is 20 years his junior, a former waitress whom he met when she was 19 and working at an LA restaurant. They married, he said, so she could travel with him to South Africa while he was making Lord Of War. "You can connect the dots." Ah, an immigration matter. He adds, "And we did it because we loved each other."

If the genders were reversed, we would be talking a lot about the age gap, in which Cage is profoundly uninterested, although Alice's family were not so sanguine. "When my mother-in-law came to the house for the first time, before even hello or nice to meet you, all I got was" – he puts on a broad Korean accent – "'She too young!' And so I knew this was going to be an uphill battle." He won her around, of course.

"I don't want to go there." Cage smiles. "I have great respect for Korea and what's happening with their industry and they're hard workers and they're doing so well. Samsung is Korean. Hats off to any country that works as hard as they do."

Cage has never spent more than four days away from his son, and is trying to figure out if it's fair to take him out of school for three weeks when he films in China later this year. Has he shown Kal Nosferatu yet? "No." He smiles. "He's on a very strict diet of animation."

Many of Cage's films would, of course, be unsuitable for his son to watch.

Cage grew up watching James Bond and realised, studying Sean Connery, that a career in action will keep you working. It's not the Oscar he won for Leaving Las Vegas, or his charming performances in Adaptation and Raising Arizona that fuel demand for him. It's the roughly $2bn in revenue grossed by his blockbuster movies, some of which he had to be talked into making. "I really didn't want to make that," he says of Moonstruck. "I wanted to make Vampire's Kiss, because I was still trying to live my punk rock dreams. I did not want to be in a big splashy romantic comedy with Cher."

And then there's The Wicker Man, the recent Neil LaBute remake that I didn't think was as appalling as everyone else did. "The issue with The Wicker Man is there's a need by some folks in the media to think that we're not in on the joke. But you don't go around doing the things that character does – in a bear suit – and not know it's absurd. It is absurd. Now, originally I wanted to play that cop with a handlebar moustache and like a really stiff suit, and the producers wouldn't let me do it." Oh, Nic! "And then you would have known how in on it we were, Neil and myself. The fact that that movie has been so lambasted means there's an inner trembling and power to that movie. It has become an electromagnetic movie! And so I love it."

Cage's politics are indistinct. He has a libertarian edge, but also seems broadly liberal. I wonder if he has any sympathy for Jim Carrey, who last month criticised his own decision to appear in Kick-Ass II (Cage was in the first Kick-Ass movie) because of its violence. "You know, Jim's gonna do what Jim's gonna do. I believe in freedom of speech. I don't believe in putting a gag on creative expression. Don't go to the movie if you don't want to see violence. That's your choice. I hate slasher films, for example. I don't watch slasher films, I think they're disgusting. But I think it's important to live in a world where there's that freedom to create whatever it is you want to create."

Where is he on gun control?

He laughs. "That is a political question."

Right. "It's something I would love to be able to answer. But I've been very neutral. By design. I know some people look down on my quietude, but I feel it would impact my ability to be an artist. If I wanted to make a movie about it one day, I don't want you to know what side I'm on when you go to that movie. It's like I, Claudius. I know this is random, but the whole reason Claudius survived and went on to be emperor is because he was smart enough to keep quiet and to build his path. Which is what I'm doing."

And so he ploughs on. His new film, The Frozen Ground, based on the true story of a serial killer who killed at least 17 women in Alaska in the 1980s, is a good, solid drama, with Cage as the cop and John Cusack as the killer. There is something quite touching about Cage's complete failure to publicise it during the interview, although it is the pretext for our meeting.

The fact is – and one can well imagine this – that Cage says he's no good when he's not working. "It's like if you have a doberman and you don't let the dog work, it's going to get a little… hyperactive. They want to please, they want to work." He has a routine to keep him steady between jobs. "I've made a new point of reading the New York Times from start to finish every day. I watch CNN. I read the Guardian. I'm trying to take in what's happening in the world. Those become resources for me."

Is he ever in danger of feeling used up?

"I can't get used up. It's not possible, because I am open to the world." Like so much of what Cage says and does, this should be cheesy, but somehow it isn't. It's the fundamental Cage paradox: the guilelessness that makes his performance.

• The Frozen Ground is on limited release now.