Major Barbara, NT, Olivier, London<br/>Baby Girl/ DNA/ The Miracle, NT Cottesloe, London<br/>The Man Who Had All The Luck, Donmar, London

Oh what a lovely war! Shaw is back on top: Nicholas Hytner's incisive revival of this fiercely radical play takes us from society farce to a cry for armed revolution
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Clare Higgins's Lady Undershaft looks im-peccably respectable at the start of Major Barbara. In Nicholas Hytner's trenchant revival of Bernard Shaw's dark Edwardian comedy, she's a demanding upholstered matriarch. Her home is stuffed with the accessories of well-to-do comfort: brocade cushions, gleaming mahogany, porcelain knicknacks and her Harrow-educated son, Stephen, idling in white tie.

The tarnishing news she proceeds to break is that – although long-estranged from her arms-dealing husband, Andrew Undershaft – her household is dependent on his money. In fact, she has invited him to dinner because she needs to arrange allowances for her daughters and she wants Stephen to inherit the munitions firm, contrary to its quirky tradition of foundling heirs.

John Heffernan's sniffy Stephen turns up his nose at such filthy industrial lucre. So does his sister, Hayley Atwell's Barbara, because she has found God and become a Salvation Army evangelist. Moreover, when their pater returns to the nest, he stands by his wealth-making code of selling weapons to anyone who wishes to buy them.

In spite of this, an instant personal bond forms between Atwell and Simon Russell Beale's goatee'd Andrew: an almost flirtatious, Freudian family romance between the daughter and the long-lost father. The pair strike a competitive deal as well, in which each will try to convert the other to their creed. He will visit her Christian soup kitchen. In return, she'll come to his factory (which offers utopian conditions for its workforce).

Shaw can be a verbose bore, and the National certainly didn't fanfare his 150th anniversary in 2005. However, Joan of Arc proved the NT's surprise hot ticket last year and now comes this reminder of how witty and fiercely radical he could be. Major Barbara ranges from Wildean society farce of mistaken identities to what sounds startlingly like a call to armed revolution – more like Gorky.

The evening drags slightly at first. Further into the run, the dialogue will probably trip faster off everyone's tongues. Some of the minor characters need work and the over-compacted final twists in the moral battle more clarity. But the fact that Shaw's sympathies seem to slide around is disturbing, forcing you to question your own preconceptions. He gives the profiteering devil very strong pragmatic arguments against poverty, and also scorching ripostes. Decimating Stephen's naive belief in politicians' rectitude vs war-mongering and commercial interests, the powerful magnate simply scoffs that he, Undershaft, is the government.

Russell Beale is the master of the crushing pause here, bringing priceless comic timing and heavyweight punch to key speeches. He switches mercurially between down-to-earth warmth, impassioned argument, and shocking, almost satanic, cynicism. Hytner's production ultimately reverberates with the rumbling engines and whistling shells of all our future wars.

You can see Major Barbara for just £10 courtesy of sponsorship by Travelex. Now is that a good deal or what?

Disappointingly, the Cottesloe's new trio of plays for teenagers is weaker than its previous triple whammy, Burn/Chatroom/Citizenship. Lin Coghlan's The Miracle is feeble superstitious hokum, half tongue-in-cheek, about a mocked adolescent misfit-turned-healing mystic. Roy Williams's drama, Baby Girl, is a portrait of depressingly hard-bitten council-estate kids and repeated cycles of under-age pregnancy. That said, elements of hope – hope for change, innate goodness, and uncowed individualism – supply comfort in both these works. Williams has an ear for vibrant slang too, though some of the acting is awkwardly self conscious with Paul Miller's ensemble mixing the professional and youthfully amateur. A distractingly busy backdrop of video projections does not help.

With a touch of The Lord of the Flies, Denis Kelly's DNA offers the bleakest vision, with a gang passing the buck for a woodland murder. The plot is improbable. One police sniffer dog would have exposed the truth. But Kelly is the new Pinter in combining sharply honed language, cold menace and black humour.

Sam Crane is brilliantly unnerving as the almost silent, sweet munching delinquent mastermind, Phil, and Ruby Bentall is fabulously funny as his dowdy, rabbiting sidekick.

Finally, Sean Holmes's tense and haunting production of The Man Who Had All the Luck does Arthur Miller's reputation the power of good. It's refreshing to see his rarely aired early drama about a small town garage mechanic, David, who gets rich but is increasingly disturbed by his own sense of undeserved success and the fickleness of fortune. In the end, he almost perversely destroys his own happiness. Maybe the shock of the Great Depression – or of the Holocaust in Europe – lay behind this play, but certainly the nagging sense of insecurity still touches a nerve today.

Miller does keep, typically, hammering home his big theme: fatalism versus self-determination. If the doomy veteran, Shory, repeats one more time that we are mere jellyfish at the mercy of life's tides, his pals will surely have to pummel him senseless in a contrary demonstration of get-up-and-go-for-him. One could also cavil about the cast's hit-and-miss American accents. However, the combined effect of the nuts and bolts of David's garage – with its no-nonsense talk of spanners and broken crankshafts – with ghostly visitations from malignant and beneficent neighbours proves riveting. Paul Constable's lighting is thrilling, with an eerie glow emanating from the dashboard of a vintage car as David tinkers away, alone in the small hours, lying under the chassis.

Andrew Buchan works up an alarming head of steam as he goes increasingly off his trolley. Michelle Terry is also wonderful as his childhood sweetheart and wife, Hester: a beaming girl who seems to age before your eyes, growing wild and pale with grief. Worth catching.

'Major Barbara' (020-7452 3000) to 15 May; 'Baby Girl etc' (020- 7452 3000) in rep to 10 April; 'The Man Who Had All the Luck' (0870 060 6624) to 5 April

Need to know

The fall and rise of GBS: The playwright's 150th anniversary passed un-trumpeted two years ago, British directors believing him dusty and whiskery. 'Widowers' Houses' was his last proper outing at the National, in 2000. In the commercial sector, Peter Hall staged a West End 'Major Barbara', with Jemma Redgrave, in 1998, and Richmond's tiny Orange Tree dug it out recently. When 'St Joan' became the National's surprise hit of 2007, Shaw, above, was back in vogue.