If, as writer and poet Mieko Kawakami says, Japanese literature is filled with books that are “odd, cute and a bit mysterious”, then Kōbō Abe’s novels score two out of three. There’s nothing cute here, but they go right through odd and mysterious – stopping at sinister, strange and discomfitingly sexual – and out the other side. Abe, who died in 1993, is best known in this country for his early novels, The Woman in the Dunes (1962), about a man imprisoned in a pit of sand, and The Face of Another (1964), in which a disfigured guy creates a new identity beneath a mask. Despite the descriptions, they are entry level by his standards. Now we have three later novels that can only be described as deep cuts.

All share recognisable strands of DNA, which they twine around Abe’s central themes of isolation, identity and the inability to know even oneself, let alone other people. The Ruined Map (1967), translated by E Dale Saunders, which feels like a transitional work, takes the most naturalistic approach – up to a point. The narrator, a detective hired to find a missing man, gets tangled up with the man’s wife, her brother, and mysteries involving shady businesses. But our man uses an obsessive attention to objects – papers, matchbooks, patterns of traffic – to try to solve the mystery. Of course he gets nowhere, reducing a firm knot to a mess of loose ends – people are not a puzzle to be solved – and loses even himself along the way.

If there’s something of the nouveau roman to Abe’s meticulous descriptions of the objects in his characters’ worlds, there’s a Ballardian interest too in the urban environment as a container that moulds the personality. These books are set in unnamed cities, all concrete and glass, aluminium window frames and bridges over canals. In Secret Rendezvous (1977), translated by Juliet Winters Carpenter, the main character wanders out of a hospital to find that “depending on your point of view, either the street area was working its way into the hospital or the hospital was spilling out into the streets”.

He’s in a hospital because his wife was taken there by an ambulance nobody called, and now he wanders its corridors trying to find her. But this is even less of a traditional mystery than The Ruined Map: the narrator is – no other way to put this – being directed by a man with an extra penis who believes himself to be a horse. How do you follow that? Well, with an acknowledgment that the book is partly intended to be comic (and a burst of laughter is the only response to a line such as “That extra cock you have belonged to that girl’s father!”). Beneath the bafflement, Secret Rendezvous is a satire on bureaucracy and the surveillance society, with its blend of utter absurdity and complete internal consistency reminding us that Abe considered Lewis Carroll to be an influence.

This book also brings in, with force, a final Abe theme and the one hardest for modern readers to interpret. One of the characters is a 13-year-old girl whose father films her masturbating – among other, even more disturbing, content – and it’s not easy to tell whether Abe is commenting on sexual exploitation or enacting it. This queasy voyeurism is also at the centre of The Box Man (1973), translated by E Dale Saunders, perhaps the most bonkers of the lot, where a man stands not just outside society but in opposition to it, wearing a box on his head and obsessing over a young woman (“the backs of her knees were glossy and beautiful like the inside of a shell”).

It’s a story about how we become what we most hate to see in ourselves, and how devices can exacerbate our worst impulses. It doesn’t take much to draw parallels with the aggression of online culture, where we act at one remove from others, or the toxifying effects of isolation. “Hooray for monsters! Monsters are the great embodiment of the weak.” Abe’s sentences are exquisite like crystals, but you never know what shape or colour the next one will be. You can’t prepare for him; he’s a writer whose greatness lies in the fact that, as Wordsworth put it, he creates the taste by which he is to be relished.

• The Ruined Map by Kōbō Abe, translated by E Dale Saunders, is published by Penguin Modern Classics (£9.99). To order a copy go to guardianbookshop.com. Delivery charges may apply

• Secret Rendezvous by Kōbō Abe, translated by Juliet Winters Carpenter, is published by Penguin Modern Classics (£9.99). To order a copy go to guardianbookshop.com. Delivery charges may apply

• The Box Man by by Kōbō Abe, translated by E Dale Saunders, is published by Penguin Modern Classics (£9.99). To order a copy go to guardianbookshop.com. Delivery charges may apply