IoS theatre review: My Fair Lady, Crucible, Sheffield The Dance of Death, Trafalgar Studios, London 59 Minutes to Save Christmas, Barbican Theatre, London

A delightful production puts the fun – and the class politics – back into Shaw's classic

She's got it! Carly Bawden is a spirited Eliza in the Crucible's fine My Fair Lady (Geraint Lewis)

It's a perfect match, a marriage made in heaven. And I don't mean Dominic West's Henry Higgins and Carly Bawden's Eliza Doolittle. After all, they may not even get hitched.

By the end of My Fair Lady – the classic musical based on G B Shaw's 1912 play, Pygmalion – the flower girl has already walked out on the upper-crust professor of elocution once, saying he'll never see her again. While teaching her to speak like an imitation lady, this sworn bachelor has been abominable. He has regarded her as a mere guinea pig, and assumed she'll stay as his slipper-fetching dogsbody. When she returns to him at the close, suitcase in hand, he can't resist winding her up one more time.

However, she's not crushed. In the final moments of director Daniel Evans's often delightful staging, Bawden ripostes by aping West: not his accent now, but the domineering, hands-on-hips posture he has just adopted. And suddenly he is beaming, loving her fighting spirit. This woman is more like a man than he thought (to reprise a phrase from his own earlier wishful ditty), and maybe he has made her so, albeit unwittingly.

Ending thus is both charming and clever, lightly conjoining a romcom conclusion with historical awareness of Shaw's era of socialism and suffragettes – Bawden's Eliza is a second-class citizen no longer.

Evans's cast might have brought out more early glimmers of unspoken sexual attraction, and one or two of the period costumes could be more flattering. But that's nitpicking.

As well as proving he can sing in tune, West displays gusto and playfulness, whisking Bawden into a crouching tango when she cracks "The Rain in Spain". He twirls with Anthony Calf's affable Colonel Pickering into the bargain. Bawden is particularly touching when, unable to sleep and standing on the sofa in her nightdress, she sings "I Could Have Danced All Night" with the ecstatic excitement of a child at Christmas.

Paul Wills's revolving set spins us between Covent Garden Market and Higgins's leather-bound library with splendid fluidity, helped by Alistair David's joyous choreography, including dustmen who launch into jigs with ankle-clacking and waggling heads. "With a Little Bit of Luck" is irresistibly catchy.

What this production brings home is just how funny and sharp-eyed about class Shaw could be, and what a dream partnership Lerner and Loewe formed with their jaunty lyrics and lovely tunes. And theirs is the marriage made in heaven.

The honeymoon period is long past in The Dance of Death. Indira Varma's Alice greets her impending silver wedding anniversary with a sardonic, possibly scheming smile as she turns to lift the piano lid in Strindberg's portrait of a soured marriage. As she begins to play, her ageing husband Edgar (Kevin R McNally) – an ostracised garrison captain – launches into a magnificently bonkers military stomp, in full fin-de-siècle regalia, then collapses like a sack of potatoes. It's an unsettling combination of the threatening and the farcical.

The Donmar Trafalgar season, which sets out to nurture promising directors, has a small-scale triumph on its hands. Titas Halder's strongly cast production looks hellishly gloomy (as designed by Richard Kent), the couple's pokey quarters being near derelict, with its soot blackened windows. Yet Conor McPherson's fine new adaptation is lively, with some cuts and adjustments to Strindberg's text, and his melodramatic notion of devilish malignity is toned down.

Compared with heavily macabre revivals, what emerges here is an instantly recognisable and remarkably humorous portrait of a dysfunctional couple who have a deep-buried fondness for each other. They also share a dry sense of humour, even if he's a bitter, anti-establishmentarian fabulist and she fancies a more glamorous life.

McNally's bewhiskered Edgar is memorably droll, musing that a bottle of zinfandel and a nice bit of kipper can make one feel slightly less inclined to blow out one's brains. He occasionally drops his emotional defences too, gazing at Varma with tender yearning.

She, in turn, is not obviously malignant but impishly sparky, which means the games this couple play darken the more unexpectedly. Also excellent as Alice's visiting cousin Kurt, Daniel Lapaine has a kind of luminous intensity, transfixed by her. He comically endures shocking bad manners, before being transformed into a panting beast, appalled by his own sadistic fantasies.

This Dance of Death comes across as a precursor of both Edward Albee's Who's Afraid of Virginia Woolf and Sartre's Huis Clos, except there's a coda that feels touchingly like a marital Indian summer, with an almost Beckettian sense of soldiering on.

Lastly, we've all got to rescue the endangered spirit of Yuletide good cheer in 59 Minutes to Save Christmas. Devised by the site-specific troupe Slung Low, this is a mildly jolly but underdeveloped family show, lasting even less time than its title suggests. The audience is led a merry dance round the Barbican Centre's foyers, combating dastardly Professor Meanwood's anti-festive campaign. Clearly, it's a battle for hearts and minds – involving crayoning – as we re-inspire Santa's gnomes to make decorations rather than smash up toys, and perk up a Christmas fairy who's a bit depressed. All in a day's work.

'My Fair Lady' (0114 249 6000) to 26 Jan; 'The Dance of Death' (0844 871 7632) to 5 Jan; '59 Minutes to Save Christmas' (0845 120 7511) to 6 Jan

Critic's Choice

Martin Crimp's In the Republic of Happiness morphs from a dysfunctional Christmas dinner into a smug cult's platform talk. Avant-garde, weirdly gripping and droll, at London's Royal Court (to 19 Jan). In Dominic Cooke's sumptuous Arabian Nights at The Lowry, Salford, savvy Shahrazad takes on a vengeful king, armed with what she has learnt from the world of books (to 12 Jan).