In 1939, George S Kaufman and Moss Hart had a big hit on Broadway with The Man Who Came to Dinner, the story of a famous critic invited to dinner in a small Ohio town. He breaks his leg on the front porch of the family home and ends up staying indefinitely, turning the lives of the family upside down. The idea of the house guest who overstays his welcome goes back even further  at least to Molière's Tartuffe. In her new novel, There but for the, Ali Smith deploys the conceit to satirise contemporary culture  and to ask difficult questions about history, time, epistemology and narrative. The result is a playfully serious, or seriously playful, novel full of wit and pleasure, with some premeditated frustrations thrown in for good measure.

The idea is simple: a man named Miles has been invited by a casual acquaintance, Mark, to join him in Greenwich at a dinner party that Mark doesn't really want to attend, at the house of a couple he doesn't really know and doesn't really like. Between the main course and dessert Miles slips upstairs  and never comes back down, having locked himself in the spare room. Unlike Kaufman and Hart's critic, Miles turns the lives of those around him upside down not by his intrusiveness, but by his reclusiveness: he is the absent presence around which people's imagination increasingly begins to spin.

Miles's unwilling hostess is reluctant to break down the door because it is "believed to be 18th century"; instead of calling a locksmith, she calls a reporter, and shares her story: "A stranger is living in our house against our will." Miles slides notes under the door, assuring them that he has water from the en suite bathroom and asking if they would remember that he's a vegetarian; his hosts slip wafer-thin ham under the door in an effort to drive him out.

Soon, crowds are flocking to Greenwich in the hope of catching a glimpse of Miles's hand at the window, and hostess Jen is flogging T-shirts and other "Milo Merchandise". Each chapter is reflected through the perspective of a different acquaintance of Miles; none knows him well, but each has had a pivotal encounter with him, and several were at the fateful dinner party, which is described in a burlesque set-piece at the novel's centre, sending up middle-class philistinism, complacency and cruelty.

One chapter filters through the memories of May, a dying old woman who lived through the Blitz and lost a child, and whose connection to Miles remains mysterious until after her chapter ends. Another concerns Mark, the guest who brought Miles to the party: his mother, a famous artist who committed suicide when he was a child, taught him to love show tunes (she admired Ira Gershwin's "kindness" but was more critical of Cole Porter). An academic couple, one of whom also adores old musicals, bring their nine-year-old daughter Brooke with them to the dinner, to the poorly concealed irritation of their hosts. Brooke is precocious, highly verbal, delighted by puns and fascinated by the history of time at the Greenwich Observatory near her house ("Observe-a-Tory!" she crows at one point). A budding writer, Brooke becomes the unofficial chronicler of Miles's confinement, and the only one of the characters circling around him, it turns out, who has any contact with him during his stay.

Brooke's enjoyment of puns is one of the motifs linking her to Miles; indeed, pleasure in wordplay becomes a touchstone: sympathetic characters like games with words, and unsympathetic characters don't. Thus, in the middle of the dinner party, Miles announces that the team of solicitors he works for is called "Nasty, British and Short"; Anna, who bonded with Miles years before over repartee like "you can go assonate yourself", explains puns to Brooke with examples including "there's no business like slow business".

But apparent gags can also make a significant point: Anna has just left her job at a relocation centre for refugees called "The Centre for Temporary Permanence"; her bosses there told her she had "exactly the right kind of absent presence" for her job. Temporary permanence and absent presence are the novel's two philosophical leitmotifs, linking its disparate characters, dissipating plot, and dispersing reflections on the way we are now.

As with most of Ali Smith's books, the pleasures here are in the small moments, the interest she takes in the tiniest words ("but the thing I particularly like about the word 'but', now that I think about it, is that it always takes you off to the side, and where it takes you is always interesting") and marginal characters. The "central" character, Miles, remains an enigma, and almost nothing happens  a deliberate choice to frustrate the reader's expectations, and one which many readers will find quite frustrating.

If some of the set-pieces are less successful than others  the novel's central dinner party descends from burlesque into caricature, as the guests became increasingly loathsome  there are some wonderful disquisitions on our cultural idiosyncrasies. Mark feels so besmirched by online pornography that he types "something beautiful" into Google, and concludes that the internet has just produced "a whole new way of feeling lonely", an observation underscored by May's misapprehension that the internet is called "the intimate". That sense of atomisation is at the novel's absent centre, around which orbit its fleeting, appealing and painful observations on the temporary permanence of our lives.

Everyone has wanted to slope off from a grim dinner party, particularly one at which there is loud, approving discussion of mass surveillance devices dinky enough to be classed as toys, and at which the middle-class company is so anxious that the word "recession" is banned and so delightedly philistine that the cry of "don't talk arty" is taken seriously. Most people, however, simply make their excuses and head for home. It is rare that, like Miles Garth, the largely invisible character-catalyst at the heart of Ali Smith's whimsically devastating new book, a reluctant guest simply removes himself upstairs, locks himself into the spare room and refuses to come out. Ever.

It is not quite what the party's host, the egregiously awful Genevieve Lee, had in mind when she planned her annual "alternative" gathering in her elegant Greenwich home, at which she and her husband Eric's scallops and chorizo are served up to diners who are "a bit different" from the couple's normal circle; previous invitees have included some Muslims and, on one occasion, both a Palestinian couple and a Jewish couple ("That had resulted in a very entertaining evening"). But if the arrival of an unexpected and unwanted lodger is largely troublesome ("There is lovely, lovely furniture in there," Gen protests, furiously. "It is a really outstanding spare room"), then it also provides a couple of consolations: the chance to write an anguished personal-experience column for a newspaper supplement and, when that leads to hordes of "Milo" devotees turning up to surround her house, the opportunity to make a few quid.

Smith has form on these mysterious, prophet-like figures who surface like unexploded bombs, not least in The Accidental (2005), in which the terrifyingly powerful Amber turned up in rural Norfolk to wreak havoc on a creaking family's summer retreat. At first glance, it might seem that Smith simply has a fondness for disrupting bourgeois set-ups and for sending up middle-class pieties and predilections; but while that's clearly part of her project, there is an awful lot more going on. There But For The's particular linguistic obsession is puns, and while its dinner-party hosts provide one in themselves (Gen and Eric  geddit?), Smith is repeatedly drawn to explorations of language games, to the moment in which what we say slips free from what we think we mean, where the generic becomes the particular, where the identity of the speaker comes under scrutiny. Also peppering her studiedly fragmented narrative is a series of knock-knock jokes, with the existentially problematic question "Who's there?" Who indeed?

A collection of characters  each of them in some way bewildered by that last question  gather around the central locked-room mystery. There is Anna Hardie (who also figures as Anna K, in echo of Kafka, and Anna Key, in echo of the Sex Pistols), a Scottish woman who briefly knew the youthful Miles when they were both teenage competition winners. Until recently something called "senior liaison" (meaningless titles and organisations recur: Gen is a personnel welfare co-ordinator, her husband works for the Institute for Measurement and Control), her job has been to precis the stories of the traumatised so that they will fit on one side of a sheet of paper. "You have exactly the right kind of absent presence," her supervisors tell her, as they promote her to the position of making redundant those who can't reduce so neatly the appalling stories they hear.

Mark, a gay man whose long-dead artist mother speaks to him in irritating rhyming couplets ("Silence of the grave my arse", he remarks to himself), is linked to Miles by virtue of meeting him at a performance of The Winter's Tale in which a mobile phone trills at the crucial moment: Mark is appalled, while Miles is entranced by the synchronicity of a ringtone sounding at precisely the moment in the play in which two characters most need to speak to one another. Elsewhere, an elderly women lies dying in a hospital bed, determined to retain her grip on reality for long enough to avoid being sent to a grisly nursing home. And then there is Brooke Bayoude, a garrulous, inquisitive, free-punning child who pops up asking inconvenient questions at inconvenient moments, who worries away at the problem of what actually constitutes a fact and, therefore, history, and whose comical solemnity perhaps suggests most strongly the spirit in which Smith intends her jigsaw puzzle of stories to be read.

All of these characters, Miles included, are marked by their tendency towards solitude and introspection. The internet, Mark reflects, presents us with "a whole new way of feeling lonely, a semblance of plenitude but really a new level of Dante's inferno, a zombie-filled cemetery of spurious clues, beauty, pathos, pain, the faces of puppies, women and men from all over the world tied up and wanked over in site after site, a great sea of hidden shallows. More and more it was becoming the pressing human dilemma: how to walk a clean path between obscenities." But immediately after these thoughts occur to him, he is struck by a terror that he has actually spoken them aloud; at another moment, he worries that he might make "the terrible mistake of not just seeming to be but actually being sincere".

In a novel filled with time-slips (it is no accident that most of its action takes place in Greenwich, or that Brooke amuses herself by running up the hill to the observatory as quickly as she can, as if to outwit time itself), identity shifts and language gaps, its most empathetic and sympathetic characters are all attempting to find ways in which to experience and express sincerity. One of Brooke's preoccupations is with metaphor, which she gradually understands is "just a way of saying something that is difficult to say". She also invents a variation on the word "cleverest", discovering by the book's end that it is rather better to try to be "a cleverist". It's a label that can easily be applied to her creator, who has given us, once again, a novel that is playful, humorous, serious, profoundly clever and profoundly affecting.