When Die Antwoord checked their emails on 2 February this year, among the 5,000 or so messages the group had received overnight was one from Neill Blomkamp, the District 9 director and a fellow South African. The subject line read: "Oh my god." And the message? "I fucking love you guys."

Since then, their fame has travelled further. David Lynch loves their videos so much that he invited them round for coffee. David Fincher wanted to cast singer Yolandi (stage name: Yo-Landi Vi$$er) as Lisbeth Salander in the Hollywood remake of The Girl With the Dragon Tattoo (she turned him down) and two weeks ago they shared a stage with the Aphex Twin at the LED Festival. So how did this South African "zef" rap-rave outfit, from "a tiny fishing village in Cape Town", come to be championed by hipsters the world over?

The 3 million people who've now watched their first video, "Die Antwoord – Zef Side", will be familiar with Yolandi, a diminutive blonde, and Ninja, a tattooed, lanky guy endowed with a sinuous physicality which he puts to good use as he dances and raps in an arresting Afrikaans/English hybrid. They'll also be familiar with an infamous close-up of his genitalia flapping in exuberant slo-mo beneath a pair of Pink Floyd Dark Side of the Moon shorts. Die Antwoord's name is Afrikaans for "the Answer" and at the end of the "Zef Side" video the narrator asks: "The answer to what?"

Ninja, joined by the teeny Yolandi and the tubby, mute DJ Hi-Tek, slouches against a wall, squinting. He raises his arm and lets it fall to his side. "Whatever, man... fuck." If Ninja doesn't know the original question, neither does anyone else. After the website Boing Boing seized on the video at the start of February, it was sent zipping round the globe, "taking over the interwebs", in the band's parlance, and increasing their YouTube views from around 800 to 500,000 almost overnight.

Each posting was invariably accompanied by some combination of "wtf?", "are they for real?" and "is this a joke?" Surely no serious rap could begin with: "Uh, yo, for real/ That's what I'm talking about/ Check it out", as the track "Beat Boy" does?

But for the huge crowd rammed into Berlin's Magnet club to see them, Die Antwoord are no joke. Neither, it turns out, is their live show. Their set has the whole crowd thrashing and rapping along, often in Afrikaans, to every word. When they can keep up, that is, because Die Antwoord's outrageous aesthetic makes it easy to overlook just how good Ninja is. Relishing its guttural smacks and hard edges, he makes Afrikaans sound like a language that was made for hip-hop. It's testament to his charisma, too, that he can mutter an incidental "fokken fok" into the microphone and elicit the kind of audience reaction worthy of Martin Luther King.

When not rapping, he shoots bug-eyed glances to his sides from beneath a lowering brow, looking very much like a pre-Country Life John Lydon. Meanwhile, Yolandi, sullenly passive in the videos, is ferocious on stage. At one point, she yells: "Germany! Now you've fokken heard of me!" They've more than heard of her – at least three women in the crowd sport her haircut: an uncompromising combination of undercut and mullet, with a brutally short fringe. "The Yolandi" may yet become 2010's hipster equivalent of "the Rachel".

At one point, the pair lead the crowd in a chant of: "Jou mae se poes in a fispaste jar", which Ninja translates, politely, as "your mother's private parts in a fish paste jar". Their lyrics get much filthier than this. So filthy, as Yolandi will tell me later, that when they first became famous, "all these conservative Afrikaners thought we'd sprung from Satan's dark pit".

My interview was originally postponed due to an ominously vague explanation: "Ninja's being... difficult." The band's publicist tells me the last journalist used the phrase "white trash" and called Ninja by his real name (the incongruously grand Watkin Tudor Jones). She closes her eyes and shakes her head, as though his reaction was too horrific for words. None the less we venture, with some trepidation, up a dark staircase to meet them.

Backstage, in a brightly lit room, Ninja is holding court while eating pitta bread and hummus. He clasps both my hands and does a little bow and a series of ingratiating head tilts, an odd and endearing courtly dance that's repeated when we say goodbye. Gesturing to their rider – tiny dishes of prunes, nuts and sweets: were it not for the Jägermeister bottles, it could be a table set for a children's birthday party – he gabbles: "Have some food, it's all free!"

Complimentary peanuts may soon lose their thrill, but for now, you can't really blame them for getting excited. Die Antwoord are not the first hip-hop group to inject humour into what they do. They are, however, the first rap-rave group from South Africa to become a global phenomenon, delivering a slap in the face to anyone moaning about the homogenisation of culture or the pervasiveness of Anglo-American pop music.

When I meet them the following week in London at their record label – they're newly signed to Polydor – they're hunched inside their own-brand tracksuits looking morose. Then Ninja starts expounding on the meaning of "zef" and he comes alive. "It's like the underbelly of Afrikaans; an embarrassing thing they want to hide away. The zef swearing, for me, is so fucking extreme that it's like cartoon language – this weird, like, freak mode fungus style. Because it's not just a language, it's..."

A whole culture?

"Ja and we just, like, dived into that and made that our thing."

"Zef's kind of like you don't give a fuck and you have your own flavour and you're on your own mission," says Yolandi. "It's associated with people who soup their cars up and rock gold and shit. Zef is, you're poor but you're fancy. You're poor but you're sexy, you've got style."

Ninja – or rather Watkin – has long been involved in hip-hop groups ("I've been fucking around with lots of, like, conceptual stuff for a while"), but the thinking behind Die Antwoord, as the 36-year-old explains, "was kinda throw away the conceptual stuff and just let it be South Africa and South African style. Yolandi sort of pushed me because it was right there and sometimes you can't see what's right in front of your face". Yolandi, whose age remains a secret, "was doing nothing" before Die Antwoord except, as Ninja adds with some pride, "causing trouble, going to rehab and getting expelled".

Ninja's engaged in an anecdote about their beef with one of the producer Diplo's DJs when he lets slip that he has a daughter. A daughter? "Ja, ja" he says, impatiently. With Yolandi? "Ja, we're just friends, but we had this kid by accident. We're a good fucking mum and dad on that level, whatever." I'm reeling at the image of either of these two changing nappies. Ninja, however, is speeding on. "A lot of people wanted to ban the interweb to stop us getting known. And you can't stop it. We've got this fierce fucking following – like the cutest, most freak-mode, wildest kids, and also older people who are super-duper in tune with what we're doing, and that's not going away – it's getting bigger fucking fast. Bigger and bigger.

"It's, like," he continues, "is this [Die Antwoord] fucking terrible, like fucking retardedly the worst thing ever or the most amazing thing in the entire universe?" I'm with David Lynch et al on the answer.