Clybourne Park, Royal Court Downstairs, London<br/>The Maddening Rain, Old Red Lion, London<br/>How to be an Other Woman, Gate, London

A new play spanning fifty years of life in Chicago reveals the truth about race relations before and after Obama

The sun is shining over Chicago, at first.

Its rays dapple the Stollers' net curtains in the deceptively idyllic suburb that's the setting for Bruce Norris's new play, Clybourne Park. This darkening comedy is bold and satirically lacerating, a drama about real estate and racism – the latter traced though half a century in this so-called melting pot.

Though different kettles of fish, the US and UK have enough parallels for director Dominic Cooke's cast to provoke howls of laughter and intakes of breath. This ensemble tread a fine line between the hilarious and seriously excruciating, even as their characters lurch from one faux pas to the next.

To begin with we're transported back to 1959. Bev Stoller (Sophie Thompson) is bustling around in a frilly apron, chattering with inane cheeriness about queer foreign place names. Her husband Russ (Steffan Rhodri) sits flicking through a copy of National Geographic. Is he laidback – tolerating her manic cheerfulness – or depressed and seething?

We gather this couple is moving soon, to be nearer his new office. In truth, however, they're trying to escape a skeleton in their closet.

The black housemaid, Francine (Lorna Brown), is helping Bev pack, politely turning down the repeated offer of cast-off knicknacks. Then Martin Freeman's preppy Karl Lindner, from the local Improvement Association, intrudes. While beaming chummily, he brings the news that the folks who've bought number 406 are (unbeknown to the Stollers) "coloureds", and the association wants the sale halted. Lindner insists the Youngers' arrival will ruin this hitherto all-white neighbourhood.

If some of those names sound curiously familiar, that's because 406 Clybourne Street is the dream home which remains offstage in A Raisin in the Sun. And Lindner was the cameo Wasp in that great African-American drama by Lorraine Hansberry, visiting the Youngers in their ghetto-like tenement, pressurising them to stay put.

Norris's drama (without requiring any knowledge of Hansberry's play) enthrallingly pictures how this crisis played out on the other side of the tracks. This playwright is eagle-eyed when it comes to subtle xenophobia. Then he engineers escalating tensions to be both farcical and alarming, with Francine and her husband (Lucian Msamati) dragged into the segregationist debate. Russ's bile, directed at Lindner, is also gloriously eruptive.

Thompson's twittering Bev hides startlingly depths of grief, and Norris's characters are unsettlingly mercurial too.

Furthermore, Clybourne Park fast-forwards after the interval to Obama's not entirely integrated US. Here the cast play new characters, on the same geographical spot but in dynamically altered relationships. A young white couple, who've just bought number 406, are taken aback when their snazzy rebuilding plans meet resistance from the now predominantly black Owners' Association.

Lorna Brown's elegant Lena (a great-niece of Mrs Younger), is ice-cool, almost supercilious. Then when Freeman's Steve – the purchaser – accuses her of covert racism, political correctness goes out the window and the two sides launch into a kind of verbal shoot-out. Each side fires off shocking racist jokes (anti-black and anti-white). This showdown feels at once deeply hostile, wildly liberated and – for the audience at least, because it's so appallingly funny – like a bonding experience.

In The Maddening Rain, by Nicholas Pierpan, it's class aggro that ultimately drives the unnamed male narrator crazy. Or is his psychotic episode sparked by a sense of lonely meaninglessness in the midst of London's rat race? Played by Felix Scott with a brooding glare, this bloke in a sharp suit recounts how he worked in menial odd jobs before becoming a cutthroat City trader.

Though Pierpan was a finalist in last year's prestigious Yale Drama Prize, alas, this monologue is not so theatrically brilliant. Isn't it really a radio play, or a novel-in-progress? More startling observations and narrative momentum are needed. Scott maintains intensity, but director Matthew Dunster merely roots him to the spot while the technical crew ring what changes they can: bursts of rock guitar; strip lights snapping on in an inner office, glimpsed through a door.

Other plays, from Serious Money to Enron, have better captured trading's hectic buzz. And Pierpan's storytelling skews off weirdly near the end, the narrator supplanted by the agonies of another character whom he has double-crossed

Adapted by director Natalie Abrahami from Lorrie Moore's short story, How to be an Other Woman left me bored and alienated. I felt no affinity whatsoever with Charlene, the 1980s material girl recounting her affair with a married man, in the wry style of an instruction manual for mistresses.

My chances of identifying with this insecure secretary might have been quadrupled since four actresses are playing her, identically dressed. In practice, though, Charlene comes over as a shallow stereotype, gaining no psychological depth by being multiplied on stage.

Faye Castelow does manage wordlessly to convey waves of anticipation and irritation as she waits, shivering, for her tardy amour. Also, some of Moore's cliches are obviously meant to be droll, Yet, what sympathy can one muster when Charlene falls for a caricatured slimeball? Jack (played by the same actresses) affects a gangster swagger in a permanently cocked trilby.

The set design – a boutique with silver racks of raincoats – is neat, but not enough sell this show. Choreographer Aline David adds some slinky dancing too, but that doesn't compensate for the dialogue's unbelievably feeble jokes.

'Clybourne Park' (020-7565 5000) to 2 Oct; 'The Maddening Rain' (020-7837 7816) to 18 Sep; 'How to be an Other Woman' (020-7229 0706) to 2 Oct

Next Week:

Kate Bassett watches her back among the Washington suits in the political thriller Blood and Gifts, at the National Theatre