The Knife's Olof Dreijer has just uttered a word that strikes fear into the heart of every right-thinking pop fan. Explaining how he and his bandmate and sister Karin Dreijer Andersson rebooted the Knife after six years of doing other things, he reveals that they started to "just meet up and jam".

Jamming? Isn't that what burnt-out old rockers do when contractual obligations force them back into the studio and they realise that they don't have any songs? But the Knife's were no ordinary jam sessions. Instead of noodling away on vintage Strats, the primary instruments at their disposal were a zither and a bedspring in a box, played with a bow, processed through a modular synthesizer to distort the sound. "After a year, we had some material that was pretty different from the Knife," says Olof, with calm understatement. "At first we talked about releasing this under another name. Then we thought it's actually more funny to call it the Knife."

He doesn't laugh when he says this – Olof and Karin are endearingly earnest interviewees – but the Knife have always got a kick out of confounding their audience. Easily their best-known song is 2002's Heartbearts, a joyous electropop hymn that propelled them on to the worldwide stage thanks to an early outbreak of blog buzz. Heartbeats also made the career of their countryman José González, who covered it in an advert-friendly acoustic style.

Conversely, their recent single Full Of Fire was electropop only in its most primitive, punkish sense, having more in common with Throbbing Gristle than Yazoo. Its brash, buffeting beats seemed designed for rioting rather than dancing, an impression matched by the lyrics' valiant sloganeering: "All the guys, and the signori/ Telling another false story", raged Karin, before declaring, brilliantly, that "liberals giving me a nerve itch". The accompanying video, by queer feminist porn director Marit Ostberg, featured cross-dressing cleaners, lesbian bikers and a woman urinating in the street. Suffice to say, José González would have his work cut out covering that one.

Although they haven't released a proper album since 2006's bewitching Silent Shout, the Knife's stock has continued to rise in the intervening years. This is partly the result of some impressive side-projects – the gothic domestic pop of Karin's acclaimed Fever Ray album; Olof's lucid techno excursions as Oni Ayhun; the ambitious, elemental and unexpectedly romantic score the pair wrote for Tomorrow In A Year, an opera about Charles Darwin – but also because the Knife's MO has been mimicked so frequently. There are now so many female-fronted electropop acts emerging from Scandinavia that it's becoming hard to keep track.

Helpfully, the Knife's startling new album Shaking The Habitual puts plenty of water between them and the pretenders to their throne. It proves that they can still write bizarre, inventive, oddly moving pop songs, but these are interspersed with passages of ominous drone lasting up to 20 minutes. Lyrically, the album takes aim at imperialist governments, phoney cultural constructs and families both royal and nuclear. It's never didactic, always poetic. But in a world where irony has superseded outrage and Carly Rae Jepsen tops critics' polls, you worry that such an explicitly political record – the inside sleeve features a satirical cartoon about extreme wealth – risks coming across as a little gauche.

"But I wonder, who are these people who think like that about music?" demands Karin. "We've done 14 or 15 interviews so far for this new album and only one of the journalists has been a woman – and that was for a feminist magazine. I think that speaks a bit for itself."

Surely, though, it's not just a few jaded male music hacks who think pop and politics shouldn't mix? Ask the vast majority of people why they listen to music and they'll say it's for escapism.

'There's a narrative that culture or music should not have to do with politics. We are learned all the time to not think' Olof Dreijer

"There's a narrative that culture or music should not have to do with politics," concedes Olof. "We are learned all the time to not think, and that of course comes through in many cultural workers. But I believe that it's in the music where you can really try out political alternatives and utopias. I have many friends who play around with these issues in their music – Planningtorock, for example, is doing that in really exciting ways – but the kind of vocabulary used around these artists is that it's pretentious or the production is not good enough. And that makes me think more about who is writing those things, as Karin said. It's not so easy to come through with a political message in music."

For Shaking The Habitual to be a truly effective political statement, the Knife felt it was important that the music reflected the same anger as the lyrics, rather than relying on more traditional songwriting to act as a Trojan horse for sneaking in the odd subversive idea. Unquestionably, it's a challenging listen at times, but the band won't lose any sleep worrying about what people who came to the band through Heartbeats might make of a 10-minute industrial noise track called Fracking Fluid Injection.

Pop music has always been about brokering a compromise between art and entertainment. Is accessibility something the Knife genuinely never considered, even when deciding on the ratio of conventional songs to experimental freakouts to put on Shaking The Habitual? "No, you just have to be true to your ideas and do the best out of them," says Karin. "You don't know what will happen, and that may be a bit scary, but it's important to not think about the reception."

Back in 2006, the Knife unnerved journalists by refusing to remove their long-beaked bird masks for interviews. This time around, they're not doing face-to-face interviews at all (this one's being conducted via Skype). "Onstage, of course we will be masked," assures Karin. Is this because they don't want anyone making snap judgments based on what they look like, or just because they enjoy dressing up?

"It's always fun to try out different roles," she replies. "I would like to quote [gender theorist] Judith Butler, who says, 'We are always in drag'. That has to do with the idea of authenticity: is there really any time when you are your true self? I would say that we're always playing a role. Even guys with guitars who sing about their emotions, they are playing a role of a person who does that."

'Sometimes I think I should get another job, and do this only for its own purpose. It's important to separate creative expression from making money' Karin Dreijer Andersson

Karin Dreijer Andersson of the Knife.

The idea of authenticity in music is something that's been bothering the Knife ever since they started getting deeper into feminist theory (Olof signed up for a course at Stockholm University's department of gender studies, while Karin borrowed his reading list). "We've tried to find ways to implement what we have learned in queer theory," explains Olof. "We are really into criticising this idea that there are some sounds that people would consider more authentic than others. And the way we'd do that would be to get sounds that you don't really know where they come from. It could be a synthesised sound or a voice or even an animal. You don't really know about the origin."

It still holds true for some people that if they can't picture anyone physically singing or playing an instrument, they can't relate to the music emotionally. "Well, we are constructed to like certain things," he continues. "We've been teaching a bit at this summer camp for teenage girls who want to make electronic music, and there we often talk about this idea of quality in music and what informs our ideas of what is supposed to be good and bad music. You know that music history is written by privileged white men, so we can ask ourselves how important it is to repeat their ideas." Bet they don't teach that at the Brit School.

It sometimes feels as if the Knife's feminist theory has an answer for everything. Don't like their new tune-free tracks? That's because you've been culturally conditioned to enjoy the decadent concept of melody. Yet it's also inspiring to hear a band talk with such intelligence about the ideas underpinning the consumption of music, rather than going with the flow in order to build a career. "I don't think you have the right to make a living out of your music-making," asserts Karin. "Sometimes I think I should get another job, and do this only for its own purpose. It's important to separate creative expression from making money."

Most bands don't make much money these days anyway, but Karin sees fresh dangers. "Bands are getting even more commercial because they are selling their music to advertisements and going on tours with big alcohol brands," she says. "That's really scary because it's hard to see how music and art can continue to develop or challenge itself within these new, very commercial frames."

Rest assured that the Knife's forthcoming tour – only their second ever – won't be sponsored by Absolut. Instead, true to the band's principles, their new stage show has been devised in collaboration with an all-female collective of choreographers and set designers. "It's important to show that it is possible to work feminist in the way you organise yourself," says Karin.

It remains to be seen whether the live show will be as eerie and fantastical as the one Andreas Nilsson designed for the Silent Shout tour in 2006, with the balaclavaed duo wielding fluorescent drumsticks. "That depends on what you find fantastic," says Karin. "I have a friend's friend who works on making live shows for big artists, and their idea of fantastic is having helicopters flying in onstage and so on." That doesn't give us much of an idea of what to expect. Will there be dancers? Lasers? Lesbian bikers and women urinating on the stage? Olof refuses to take the bait.

"It will," he deadpans, "feature at least 10 helicopters."

Shaking The Habitual is out on 8 Apr on Brille; the single A Tooth For An Eye is out now