1Q84, By Haruki Murakami

(Rex Features)

How odd, but apt, that an author who writes so often and so well about the lure of cults should himself have become the idol of a worldwide sect of votaries. Near the end of the first of the three volumes that make up Haruki Murakami's 1Q84, a policewoman who has investigated a secretive commune reports that "Doctrine-wise, it's kind of deconstructionist". Initiates absorb "a jumble of images of religion" that takes in "new-age spiritualism, fashionable academicism, a return to nature, anti-capitalism, occultism, and stuff". Overall, their creed "has a bunch of flavours, but no substantial core". Ayumi, a traffic cop who likes to pick up strangers in the company of the novel's heroine and enjoy "all-night sex feasts", adds: "In McLuhanesque terms, the medium is the message. Some people may find that cool."

Intense flavours, multiple sources, eclectic forms and a "substantial core" that, if it exists, forever eludes the seeker: a global fan-base finds Murakami's medium the coolest stuff in print. Modest to a fault, its highly disciplined inventor does little to provoke idolatry. The hero of 1Q84 finds that "he could not help spending a large part of every day writing fiction"; for him, "writing was like breathing". In this, if in nothing else, he matches his creator.

Prolific, prolix, prodigious: read the book – or rather the books – and pick your preferred epithet. In Japan, the unstoppable 62-year-old marathon runner (both literally and figuratively) published the first two parts of 1Q84 in May 2009. It sold a million copies inside a month. Within a year, he had followed up with a supplement that wraps up a trilogy. Or does it? Enough loose ends still hang at the close to suggest a possible tetralogy.

The plot unfolds in and around Tokyo between April and December 1984. In Japanese, the title is a pun, ichi-kyu-hachi-yon: the "nine" sounds like "Q". Murakami hoists a big question mark over the year, and its reality. We begin on a bright cold day in April. Yes, allusions to George Orwell's dystopia crop up, but don't explain that much. The abuse of knowledge and power within closed systems matters a lot to Murakami. In addition to various fictitious cults, his first-rate reportage in Underground explored the background to the gas attack on the Tokyo metro carried out in 1995 by adherents of Aum Shinrikyo. Malignant authority here has become decentered, dispersed. In place of top-down Stalinist coercion, as in Nineteen Eighty-Four, domestic and sectarian tyrants shackle and damage bodies and minds. Dictatorship and dread have been privatised.

Two narratives run in parallel. The reader soon grasps how they connect; the characters, much more slowly. On Metropolitan Expressway No 3, Aomame leaps from a cab in her green Junko Shimada suit and chestnut-coloured Charles Jourdan heels. On the car radio, Janacek's Sinfonietta (a recurrent allusion) plays. When he wrote it in 1926, in idyllic pre-Hitler Czechoslovakia, "no one knew what was coming". Neither do we.

Aomame, whose embarrassingly unusual name means "green peas", is a gym trainer, massage therapist – and a professional assassin. Her employer selects targets with the utmost care. They are violent, abusive men who beat and rape, torture and terrify, their wives and children. An elderly "dowager" gives Aomame her commissions. The refined widow of a tycoon, she runs a refuge for battered women as well as funding this more discreet programme of corrections.

Aomame herself comes from a strict family of Jehovah's Witnesses whose stifling embrace she fled. Leggy, toned, ball-kicking feminist avenger: she clearly belongs on the manga and anime planets of Japanese pop culture. Does she also owe something to Stieg Larsson's Lisbeth Salander? As for her own pleasures, she prefers casual flings with balding middle-aged guys. Yes, really. Her erotic ideal may be the mature Sean Connery (credible) but, failing Sean, any past-it slaphead will do (not credible). We have, in so many ways, left plausibility behind.

On the novel's other track, Tengo struggles to juggle his day-job as a maths coach at a private crammer with a passion for writing fiction. In the ordered universe of maths, "figures only flow in one direction"; stories, however, "use words to transform the surrounding scene" into a human home. Thanks to literature, "I can confirm... that this person known as 'me' exists in the world". Sporty, clever, attractive, but drifting and forlorn in the manner of Murakami's leading men, Tengo feels – like Aomame – "a kind of alien" in his skin. He suspects that he is not the biological child of his taciturn and brooding father, a collector of licence fees for the NHK television network (that job spawns a wonderfully disquieting running joke).

Aged ten, at school in Ichikawa, Tengo and Aomame once held hands. In that fleeting touch, each felt urgently drawn to the other. In one sense, over its thousand pages, 1Q84 simply sets up the conditions for a second encounter. Will they ever meet again?

Tengo does odd jobs for a curmudgeonly editor, Komatsu. Within this strand, more Henry James than Stieg Larsson, he polishes up a raw manuscript submitted by a teenage girl for a new writers' prize. Komatsu wants to fool the literary establishment and Tengo, the "born technician" with a fine style but feeble inspiration, proves the perfect vehicle. "Air Chrysalis" is a weird fantasy tale by a dyslexic and withdrawn 17-year-old who goes by the name of Fuka-Eri. It marries "rough" and "clumsy" writing with a compelling vision of an alternative world in which the magical "Little People" sway human destinies. "Entirely original, and quite contagious", Fuka-Eri's imagination possesses, to Tengo, "some special kind of power".

She has been raised as the daughter of a cult leader on a rural commune. There, hippy communism and the cultivation of organic vegetables have degenerated into the fabrication of a full-blown charismatic creed: god-like leader, mind-games, thuggish security, child abuse, sinister incinerator – the works. Fuka-Eri has escaped into the care of Professor Ebisuno, a disenchanted former associate of "Leader". Now her story, which folds autobiography into science fiction, wins the prize and plunges Tengo into his own dimension of deceit.

It gets stranger (of course it does). When, miniskirt hoisted, she shimmies from the expressway down an emergency staircase on her way to terminate a wife-beating scumbag, Aomame enters a different world. She notices it first because the cops have swapped the old-fashioned revolvers she thought they carried for bulky semi-automatics. Now, two moons hang in the night sky: the normal one, and a smaller, lopsided and greenish twin. (Aomame, perhaps not coincidentally, worries about her assymetrical breasts.) This isn't a "parallel universe" of some kind: "There is always... only one reality". Rather, that reality has changed. "Blood shed in this world is real blood." But now the Little People and their fatal mischief can operate in "fact" as well as fiction.

Gradually, Tengo's and Aomame's paths begin to converge. She is tasked to close the career of Leader, prophet, guru – and, so it seems, child rapist. Meanwhile, enforcers for his Sakigake religion – "pioneer" or "pathfinder" – target Tengo as the leak who, via Fuka-Eri's fantastic confessional, has exposed their jealously-protected secrets. By the end of the second volume, after a bravura drawn-out assassination scene, Aomame spots her lost beloved in a surburban playground, gazing wistfully at the twin moons.

The third part might strike many readers as an afterthought or anticlimax. Philip Gabriel takes over at the translator's wheel from Jay Rubin. Both do sterling work in keeping up with Murakami's lurching shifts of mood, tone and register, and no gears crash with the changeover. Now Murakami re-boots the misshappen lawyer Uchikawa – a sleazy sleuth hired to spy on Tengo by the cult – and puts him centre-stage. Sympathetically seen, he too belongs in the camp of outsiders: another "foreign element" suffering in internal exile.

But too many recaps slow the action. Since Murakami does nothing by halves, it makes as much sense to blame him for baggy repetitions as to ask Proust (whom Aomame reads in a safe house) to cut the fancy ornament and crack on with the plot. Yet, in terms of more conventional criteria, he can excel whenever he wants. Elegiac, mysterious, moving, sections such as Tengo's relationship with his father – who, stricken with dementia, moulders in a seaside sanatorium – are quite magnificently done. Scoffers or sceptics might sample the parable of the "Town of Cats" and Tengo's trip to the clinic (Book Two, chapter 8) before they dismiss this author as no more than a trend-surfers' fad.

Murakami really does stand alone, as much a "foreign element" as his heroes: a sport, an outlier, sui generis, inimitable, if often imitated. Which other author can remind you simultaneously of Fyodor Dostoyevsky and JK Rowling, not merely within the same chapter but on the same page? Viewed through the "postmodern" lens, his exemplary blend of a light touch and weighty themes, of high literature and popular entertainment, ticks every box. Posh and pop, sublimity and superficiality, history and fantasy, trash and transcendence: they switch positions and then fuse as the metaphysical speculations of an Ivan Karamazov meet the death-defying adventures of a Harry Potter.

Although 1Q84 might look too massive as a gateway into his work for Murakami novices (they could try Kafka on the Shore, Norwegian Wood or the stories of Blind Willow, Sleeping Woman), the pages scoot along at a pace that even the simplest Man Booker judge might enjoy. Too much can be made of his ineffable "Japaneseness". I would point to an affinity between the role of the Little People, who balance good and evil in the mortal world, and the Gnostic traditions of Western esoteric belief. Murakami twice nods to the Gnostic-influenced Carl Jung, for whom "There is no shadow without light and no light without shadow".

Meanwhile, the other world with its second satellite reflects the transforming power of story-telling itself, and of love as the shiniest story of all. The epigraph of 1Q84 comes from the song "Paper Moon", with Harburg and Arlen's lyrics about a "phony" world that "wouldn't be make-believe/ If you believe in me". Against the "magnificent imaginary building" of maths, Tengo finds in the story-world of Dickens – a strong presence here – "a deep, magical forest". "In the forest there were no maps", but to find love and truth we must all go into that dark. "Paper Moon", by the way, featured in a 1933 film called Take a Chance.

This folkloric element shares its appeal with the children's and SF classics that haunt 1Q84. Aomame's portal on the highway recalls Alice's rabbit-hole to Wonderland – another sporadic reference-point. In a universe with "a serious shortage of both logic and kindness", the moon – or moons - of fiction bathe lost and lonely humanity in a healing, unifying light. "Nobody would take the time and effort," thinks the bemused Tengo as he watches the altered heavens, "to hang a fake moon in a real sky". Nobody, except a novelist.