Kosovo-born Finnish writer Pajtim Statovci’s debut novel begins with a chap called blackhetero-helsinki prowling the internet in search of “fun and games”, continues with a lonely immigrant student getting into a relationship first with a boa constrictor and then a haughty cat he meets in a bar singing along to Cher’s Believe, and ends with a series of ruminations about the violence of men, of memory, of migration. If this sounds whimsical, don’t worry; My Cat Yugoslavia is a striking work about dislocation and estrangement that moves between science fiction, comic fable and trauma narrative without ever settling snugly into any of them.

The lonely student is Bekim. His parents came to Finland from the Balkans during the 1990s. When people ask him his name he often makes one up. Sometimes he pretends to be Russian. Local toughs would spit on his face: “Wipe it away and you’re dead, they said, wipe it and you’re dead, you fucking parasite refugee.” He’s mostly gay, obsessed with cleaning, and disconnected not only from his fellow students but from his mother, Emine. She too is struggling: brought up in a quietly conservative village near the Kosovan capital of Pristina, she was married off to a man whose name, Bajram (“celebration”), belied his fierce temper, and it has taken her decades to pluck up the courage to leave him.

Their stories unfold in parallel. Emine, growing up at the tail end of Tito’s regime, is lively and hardworking. She’s indifferent to the news on the radio and dreams of being an actor. During her wedding she is one; her mother teaches her how to emote properly, although, always prone to heretical feelings, she admits wanting “to pull my hands away and wipe them on the hem of my skirt, because my hands soon stank of the grime on the guests’ hands, of ingrained sweat and old grease”.

Nearly 30 years later, Bekim also finds himself struggling with desire. His cat companion isn’t the winsome moggy of internet memes; he may trill along to Bruno Mars’s Grenade and be an astute literary critic (of Günter Grass’s Cat and Mouse, he yawns: “I’m bored with such absurdity”), but he’s also lazy, patronising and homophobic. Bekim is effectively in an abusive relationship.

It’s tempting to think Statovci’s interest in migrants and animals is fuelled by a belief in their shared marginality and outsiderdom. The snake that Bekim brings into his apartment is both foreign and fear-inducing; most of his days he spends cooped up in a terrarium, just as many of the Kosovans in Finland felt penned in at their reception centres and gawped at when they stepped outside. Is the cat really aloof or is it afraid of exposing its neediness? These relationships are as visceral – the boa constrictor’s intimacy crushes, almost asphyxiates – as those of family and home country. War destabilises and mangles identity – “We were vagrants,” Emine says. “We were stuck between the truth and the lies. We no longer knew what was real” – and it’s in these bizarre, intense interactions with animals that the reader gets a feel for the hybrid nature of migrant life.

All of the characters have mixed feelings about Finland. It’s a refuge from the bloodletting back in Kosovo and a prosperous nation to which locals say they should feel gratitude. To Emine, though, “Finnish sounded like a colourless, inexpressive language. The words seemed to crack like brittle, unhealthy bones.” There are religious tensions with Bajram, who identifies as a Muslim more than he ever did back home, and is forced out of a teaching job after he objects to his school’s multi-faith syllabus.

There are passages – particularly those set in rural Kosovo – in which My Cat Yugoslavia verges on the folksy and anthropological. More often, and in no small part due to David Hackston’s elegant translation, this is a memorably disconcerting novel, a kind of literary Let the Right One In; a book about skin and sweat and the ruptured blisters of history.

• My Cat Yugoslavia by Pajtim Statovci is published by Pushkin Press (£14.99). To order a copy for £12.74 go to guardianbookshop.com or call 0330 333 6846. Free UK p&p over £10, online orders only. Phone orders min p&p of £1.99