Big and Small, Barbican Theatre, London / The Radicalisation of Bradley Manning, Cardiff High School, Cardiff / Misterman, NT Lyttelton, London

Blanchett pumps life into a play with no heart

Is Cate Blanchett hallucinating? In the opening scene of Big and Small – Botho Strauss's radically fractured play from the 1970s, aka Gross und Klein – her Lotte slurps a tangerine cocktail, looking slightly dishevelled. She sniffs her armpits and sprays clouds of scent as she yaks away, in an earthy Australian accent, about the amazing – AMAZING! – guys she can (supposedly) hear outside her hotel window. What are they saying? Something about the need to think the unthinkable, about patterns of greed, about there being 1,260 days before the termination of mankind, about how the fields will invade the empty cities.

This production by Sydney Theatre Company (of which Blanchett is joint artistic director) is off to a winning start, investing German avant-gardism with raunchy satirical humour – using a new English version by Martin Crimp, directed by Benedict Andrews. Blanchett's Lotte has a touch of Bridget Jones and Edna Everage as she yelps about the guys' seductive voices.

Perched on a white sill with a chasm of darkness behind her, she is on a strange, lonely odyssey, slipping into a dreamlike mental breakdown, principally because her husband, Paul, has left her, and virtually everyone she encounters is either cold, fickle and self-centred – or reeling drunk.

Pale walls, in slivers, glide through the darkness to form shrinking and expanding rooms. Oddly popping up outside the bedroom of a sad husband and snarky wife (a reverse image of her own life), Lotte tries, but fails, to befriend them. Suddenly she's walking through a door, over and over again, into a string of wrong apartments: farcical, nightmarish encounters with a monstrous, druggy slattern; someone who scuttles like a cockroach; Robert Menzies' Paul, in leather trenchcoat, sucking on another woman's fingers. Friends and family offer no solace. Lotte is reduced to homelessness and rifling through bins. Only a stranger's kindness offers a chink of hope.

Blanchett's performance is a tour de force, sometimes quietly intense, sometimes dancing like a jittering rag doll. Overall, this is a world-class production, yet Big and Small rarely touches the heart, the play's episodic structure offering diminishing returns as it stretches to nearly three hours. The stream of two-dimensional characters leaves you hankering for depth; the philosophical concerns are never really pursued. Is Lotte's obsession with Paul a metaphor for a riven Germany? Her desolate cries seem merely personal here.

The Radicalisation of Bradley Manning, premiered by National Theatre Wales, comes with a disclaimer. This is not an entirely factual biography of the 24-year-old American Army intelligence analyst now facing a court martial, accused of passing secret documents to WikiLeaks. Some characters and incidents have been imagined by playwright Tim Price, though it's true that Manning went to secondary school in Wales.

Making up stuff could be misleading in a production that has the veneer of docudrama. But using several performers (male and female) to play Manning in turn makes clear that this isn't a portrait set in stone so much as a multifaceted attempt at a life. (An interactive website also offers more background information and live streaming of the show on tour.)

Price's scenes cut back and forth in time, picturing Manning being bullied both in the US army and at his Welsh comp as a geeky, suspected gay. Yet he is taught about inspiring Welsh radicals too, not least the cross-dressing Rebecca Rioters of 1839. People he meets rebuke him for being moody and arrogant. The play also shows the worm turning with a righteous, mounting anger at personal and international injustices. In spite of the disclaimer, this is a powerful, not to say radicalising piece of theatre, ultimately inspiring sympathy.

John E McGrath's production, after an underdeveloped promenade through echoing school corridors, soon becomes snappy and tense, with a terrific young cast – especially Harry Ferrier, Kyle Rees, Matthew Aubrey and Anjana Vasan. An upturned table serves for a prison cell, and encircling computer screens flicker with the notorious leaked footage of the 2007 Baghdad airstrike, seen through the gunsight of an Apache helicopter.

Lastly, in Misterman, transferring from Galway to London's NT, we have Cillian Murphy's solo performance as a whole bunch of small-town Irish caricatures – written and directed by Enda Walsh. In dirty cagoule, sandals and socks, Murphy's Thomas is a religious nutter. He intends to save his loutish and lecherous neighbours from sin and imagines meeting a lady-angel. However, he's clearly psychotic and in some kind of purgatory, re-enacting old conversations and fantasies, cassette machines whirring in a vast concrete warehouse – a derivative fudge of Krapp's Last Tape and Stones in his Pockets. Run a mile.

'Big and Small' (0845 120 7511) to 29 Apr; 'The Radicalisation of Bradley Manning' ( bradleymanning); 'Misterman' (020-7452 3000) to 28 May

Critic's choice

Terence Rattigan' s The Browning Version – starring Anna Chancellor and Nicholas Farrell – gets a deserved West End transfer in an excellent Chichester Festival double bill about the repressions of boarding-school life. David Hare's The South Downs (above) is its contemporary other half. At London's Harold Pinter Theatre (to 22 Jul).