Random, Royal Court, London<br/>Testing the Echo, Touring<br/>The Deep Blue Sea, Touring

Take this soundbite: "Yu late down, porridge ha fe bu'n./Heh./Him watch the pot/ watches me watchin/sights the juice – carton done/ draws some milk – only glasses it/cah him see me watchin."

It may take a while to tune in to random by debbie tucker green (and, yes, the lower-case names are REALLY ANNOYING). Nonetheless, her free-verse plays do prove remarkably compelling. In Sacha Wares' fearlessly understated production of this new piece – about an ordinary day that turns into a family tragedy – a lone black actress stands downstage. There's no set. The actress, Nadine Marshall, doesn't even walk around, yet she is dramatically enthralling.

She's playing multiple characters and is verbally shuttling between snatches of dialogue and vividly descriptive internal monologues. So, in the speech above, she is the family's mum, with a Caribbean accent, initially rebuffing her son's backchat about the shortcomings of breakfast. Soon after, he slouches off to school, late and grinning. Little does she know that, later, the police will be knocking at her door, grim-faced.

Without caricaturing, Marshall morphs effortlessly from the tutting matriarch, giving her cardigan a prim tug, into her teenage boy with loose jiving arms, and into his tetchy older sis at work, suffering office small talk with a forced smile. Wares brings out the warm humour – and the close is poignant.

In between, when tragedy first strikes – with a violent crime, and media interest – tucker green steers close to cliché. Certain phrases are hard to catch, too, but the language is enjoyably rich, blending the highly stylised with slangy chat. The handling of suspense is also sharp. Recommended.

Testing the Echo centres on immigrants studying for the new British citizenship exam. Maybe David Edgar aimed to reflect how our nation is a multicultural miscellany, but his docudrama feels bitty. It's a medley of extracts from the exam handbook, blogs, interviews with émigrés, civil servants and historians, plus mini-dramatic scenarios – a lapsed Muslim held hostage, a white middle-class dinner party, a classroom clash.

Still, Matthew Dunster's staging for Out of Joint is slick, with lightning costume changes by Teresa Banham and company. Even if you learn no very coherent lessons, the strain that liberal tolerance is under, facing religious fundamentalism, is brought home. It is unnerving to discover, from the examination questions, how blithely uninformed most of us are, and the Home Office's laughably piecemeal notions of Britishness make you laugh – then seriously wonder what, if anything, we all really share.

Finally, in Terence Rattigan's 1952 classic, The Deep Blue Sea, Greta Scacchi's Hester outwardly tries to maintain an old-fashioned stiff upper lip while being, privately, on the skids and suicidal. She has quit her respectable marriage for a doomed passionate affair.

Scacchi is only sporadically harrowing. Still, Edward Hall's production, set in a mournfully seedy boarding house, boasts fine and touching performances from Simon Williams as Hester's stiff-backed but tender husband, from Dugald Bruce-Lockhart as Freddie, the wag, and from Tim McMullan as the struck-off doctor from upstairs – a creepy cynic or a strange guardian angel?

'random' (020-7565 5000) to 12 April; 'Testing the Echo' at Oxford Playhouse (01865 305305) to 22 March; 'The Deep Blue Sea' at Theatr Clwyd, Mold (0845 330 3565) 24 to 29 March