Andromaque, Silk Street Theatre, Barbican, LondonAlphabetical Order, Hampstead Theatre, LondonNocturnal, Gate Theatre, London

A classical tragedy with subtitles is gripping, while a 1970s British farce is showing its age

If you call your company Cheek by Jowl, then warmth and vitality are paramount. On this basis, some may reckon Racine's neoclassical tragedy Andromaque, performed in French, with English surtitles, an odd choice for director Declan Donnellan. Traditionally, Racine is thought coldly marmoreal for his relentlessly rhyming couplets, his rules of "bienséance" (propriety) and his geometric configurations of obdurate, unrequited lovers.

Electrifyingly, though, what Donnellan's actors (touring from Paris's Bouffes du Nord) bring out is the visceral fury of the thwarted royals in this post-Trojan War drama. The Greek victor Pyrrhus becomes infatuated with his captive, Andromaque, and his enraged fiancée, the Spartan princess Hermione, seeks vengeance.

This staging in the Barbican's newly commandeered Silk Street auditorium has its stark symmetries, too, with lines of wooden chairs in a vast dark square traversed by corridors of light. Designer Nick Ormerod's 1940s black dresses and military uniforms are elegantly severe.

At the same time, the actors are emotionally ablaze. Their exchanges are fast and feverish, more spat out than spoken . Christophe Grégoire's Pyrrhus, though sleek with brilliantine, has a vulpine ferocity as well as tenderness. Camille Cayol's youthful Andromaque dashes from corner to corner, outraged and traumatised. She also has one moment of bienséance-busting eroticism, in a lap-straddling clinch – forced to succumb to Pyrrhus to save her son from being put to death.

Nor is the boy kept off stage to be merely discussed. Instead, he is a constant presence. Clutching a toy Action Man, he's a confused adolescent preoccupying both his mother and her suitor, roughly handled as they snatch him from each other's arms.

Meanwhile, Oreste is obsessed with Camille Japy's Hermione, a posturing society beauty with a glazed smile that cracks to reveal a shrieking hysteric. She overeggs the satire slightly and the tension sags midway, but mostly the evening is brilliantly paced, like a piece of impassioned music, and Donnellan locates veins of sly humour. Grégoire's Pyrrhus even has a hint of Sarkozy: pint-sized and suave, more aggressive than diplomatic, and letting politics go hang when he wants a romance.

Lucy is at the nexus of three potential love triangles in Alphabetical Order, Michael Frayn's 1975 comedy set in the cuttings library of a provincial newspaper. In Christopher Luscombe's revival, the archive is a jungle of green filing cabinets. Yellowing broadsheets are strewn over the floor amid a windfall of discarded coffee cups.

Imogen Stubbs's cute Lucy – the hippyish librarian – is struggling to manage as various staff writers use this niche as a bolt hole. So, a new assistant, Chloe Newsome's frosty Lesley, is hired to impose order. Will she ultimately eradicate the humane spirit of the place, or save the business from folding?

In this office drama – part of Hampstead Theatre's "golden oldies" anniversary season – Frayn is broadly interested in how societies alternate between easy-going liberalism and stricter regimes; more specifically, the library's new broom is a curious mix of the young Maggie Thatcher and a radical union leader.

For sure, the play is passé in terms of today's internet-led crisis in the newspaper industry. The distant clatter of typewriters in Luscombe's staging underlines this is a period piece. What's more disappointing is that Frayn's evident affection for old-school journos – whom he knew from his Manchester Guardian days – doesn't produce a brilliant night at the theatre. Frayn's funnier and more tightly structured farces, Donkeys' Years and Noises Off, were still just a twinkle in his eye in 1975.

As for Nocturnal by Juan Mayorga – allegedly a top contemporary Spanish playwright – one can only hope everything has been lost in translation. Paul Hunter is meant to be a menacing nerd as Short Man, the xenophobic neighbour who befriends Justin Salinger's beleaguered Tall Man. Hunter is just a blank-faced, monotonous bore, though, in Lyndsey Turner's clueless premiere, with dull cartoon backdrops. Short Man's unhappy wife suffers from insomnia. Unbelievable, given the mind-numbing company she keeps.

'Andromaque' (0845 120 7550) to 2 May; 'Alphabetical Order' (020-7722 9301) to 16 May; 'Nocturnal' (020-7229 0706) to 16 May