Throughout his career, Jesse Eisenberg has been known for his clever portrayals of anxious nerds. Should you have a script that calls for an awkward but sweet twentysomething and want an actor who can bring more depth and a bit more sex appeal than Michael Cera can provide, then it's Eisenberg's agent who you call.

But of late, he has been accruing a very different kind of reputation: the nightmare interviewee. Back in May he met up with a young female reporter and proceeded to have what is already being touted as a classic awkward interview. It confirmed in many people's minds that, as Buzzfeed put it: "Mark Zuckerberg and Jesse Eisenberg don't seem that different at all."

Things haven't improved much since. One recent interview in a British magazine started: "I don't think Jesse Eisenberg and I will be friends on Facebook." Another dismissed him as "now more annoyingly awkward than Michael Cera".

So I wasn't sure what to expect when I went to meet Eisenberg in a grimly anonymous London hotel to talk about his latest film, the magician adventure drama Now You See Me. Charming geekishness or aggressive douchebag? At first, it looks like I might not find out because he has, according to a nervous PR woman, "gone missing".

Eventually, they find him and hustle him into the hotel room. But Eisenberg appears utterly unaware of the fuss around him, instead staring intensely at his phone and continuing to do so for several minutes after the door is shut, holding up one index finger, the sign that he'll be just a minute and I should be quiet. Eventually, though, I get bored.

Is everything OK? "It's just – these people – the timing – it doesn't make sense," he laughs ruefully to himself. "It's just – anyway. But – what? We shouldn't talk about this, I'm probably being rude."

It turns out that what Eisenberg is marvelling at is an email saying that his widely praised play, The Revisionist, which starred him and Vanessa Redgrave and recently finished its off-Broadway run, is moving to Broadway even sooner than he had expected.

"It just doesn't make sense …" he continues to mutter to himself. But that's good news, right? "Oh yes, good news," he agrees with no sign of joy.

Henry Barnes, Peter Bradshaw and Catherine Shoard review Now You See Me guardian.co.uk

While Eisenberg is gaining A-list status, the theatre, he says, is his main interest. Is he happiest writing plays? "I'm happiest rehearsing a play – I wish we didn't then have to show it to an audience but I understand an audience has to be there in order for the play to survive," he concedes with reluctant pragmatism.

So will he get to the point one day where he'll just write? "No, because I think you need to have life experiences to write and writing on its own is very isolating. Acting forces me to socialise, which is good for me, I think," he says, with the enthusiasm of child talking about having to eat his vegetables.

Eisenberg is so pale and slight beneath his oversized baseball hat that he looks more like a malnourished teenager than an astonishingly productive 29-year-old. Ever since his break-out role in The Squid and the Whale, as the older brother who misguidedly believes in his father's self-mythologising, there has never been any doubt about his acting clout. In the 1980s coming-of-age story Adventureland, he was irresistible as the virginal college grad forced to work at a theme park for the summer. He continued to work this "charming and funny" schtick in Zombieland, alongside Woody Harrelson. But it was his performance as Mark Zuckerberg in The Social Network in 2010 that pushed him out of the indies and into the stratosphere of Oscar nominees.

I tell him that when I watched the Oscars that year his expression as they read out his category reminded me of my male cousins when they came to my batmitzvah.

"Yeah! That was exactly what it was like – 'When will this end?'" he agrees with a bark of laughter.

Did he enjoy the Oscars experience? "It's just very time consuming," he replies, sounding as if he's talking about doing his taxes. "You're there to promote something but also to sell yourself which is in itself a nebulous concept." The more he talks about work, the further he pulls his baseball cap down around his curls.

His recent play was about a young man exploring his eastern European Jewish heritage – "narcissism dressed up as history" is how Eisenberg dismisses this personal interest of his – and he has specialised in playing nervy, nerdy characters. So, does he worry about being typecast as the neurotic Jewish guy, one of Hollywood's most beloved and reductive tropes? The baseball cap comes flying off.

"That's something I'm very aware of," he says enthusiastically, making eye contact for the first time. "I've turned down a lot of plays and movies where that character is done badly. When it's done well it can be great, but when it's done by someone who's just reusing the tropes, then I find that really offensive and I just …" he stops and shudders. "But I've thought about this a lot and those kinds of characters I've played have tended to have some kind of twist to them."

Like his portrayal of Zuckerberg? The baseball cap goes back on. "Yeah, that wasn't really an impression of him. I can do one but the film-makers didn't want that." They wanted something more extreme? "Yeah, exactly. But it was an interesting character."

Eisenberg is like a combination of an arrogant, highly intelligent teenager and a man who has never been properly socialised. His speech rhythms are even more jittery than they are on screen and will occasionally screech to halt for no apparent reason. To complain that he isn't always polite feels irrelevant: Eisenberg seems to dwell on a different mental sphere, one far away from conventional niceties.

Spending time with him makes his performance in Now You See Me seem all the more astonishing. The film is so-so, despite its blue-chip cast (Eisenberg, Morgan Freeman, Michael Caine, Woody Harrelson, Mark Ruffalo), the director far more interested in jazzy effects than the actors. But Eisenberg is the best thing in it, playing a self-assured and sexy ladies' man with smooth patter and very self-assured about his professional skills. The only way Eisenberg could play a character further from his real personality would be if he played an entirely different species.

"I took the part because the character is so confident in what he does. I'd been in this play, playing a character who was so insecure and I was getting terrible stagefright. So I thought, OK, let's play someone who is so confident about what he does, and it was great! I didn't have any anxieties at all. Fantastic," he muses.

Eisenberg grew up in Queens, New York and New Jersey, the only son of a college professor and a professional clown who worked at children's parties. "My mom would get up so early to practise [her clowning] and it probably seemed to other people like she was doing something silly, but she taught me the dedication needed to do something creative," he says. He was, and remains, very close to his parents.

Acting became a way to help the thoughtful, anxious teenager make sense of the world and fit in at school. It also soon became his career. By the age of 13, he was appearing on Broadway. "I was terrified of everything as a kid and that's partly why I started acting in plays, because you're operating then within a world with a set framework."

Is acting still easier than life? "Oh yes, definitely. But what I really love is writing because then you're still operating within a framework but also creating it. But also as an adult you learn mechanisms to deal [with the world] and that helps."

And therapy? "That helps, too."

What do you get out of it? He pauses and opts for the smart-aleck answer: "A captive audience for an hour a week."

He thinks again about acting: "It is hard, because I was playing a character in a play recently who was so angry all the time. So all day, every day, I'd be feeling angry and then I would get release at night [when the play finished], but then I'd have to do it again.

But if you started acting as a way to get outside of yourself, I say, it seems like it now works in reverse and the parts you play take over your personality.

He shoves the baseball cap firmly down again: "Yeah. But I'm within in the framework. So it's OK."