Deathtrap, Noel Coward, London<br/>Tiny Kushner, Tricycle, London<br/>Bedlam,Shakespeare's Globe, London

Simon Russell Beale is outstanding in this revival of Ira Levin's 1970s thriller as a fading writer who hatches a treacherous plot to revive his reputation

You would have to be Houdini. Whether you're the murderer or the potential victim, escaping unscathed doesn't look like an option in Deathtrap, Ira Levin's comic thriller from the 1970s.

Sidney Bruhl (Simon Russell Beale) is lolling against his writing desk, thumbing through a script, in Matthew Warchus's major West End revival. Bruhl is a Broadway dramatist (an ex-pat Brit in this production), with a timber-framed mansion in rural Connecticut. He's been moonlighting recently, teaching the odd masterclass, and now an eager-beaver graduate, named Clifford, has sent him this first-draft script, hoping for feedback.

All innocent enough? Heck, no. Bruhl is a wily and financially desperate crime writer, we soon glean. Not having had a hit for years, he's been uncomfortably living off his wife Myra's savings. Now he is hatching a real-life plot involving sudden death and dastardly plagiarism. The beginner is going to meet a grisly end, surely, for Clifford's chiller-killer drama is a humdinger. It's going to be a money-spinning dead cert, for whoever claims they wrote it.

Thin shoulders hunched under her sateen blouse, Claire Skinner's Myra lurks in a corner – scared rigid or a sinister accomplice – as her spouse dials Clifford's number. Beale looks like a baleful toad, though his tone is casual, as he asks the young man to come over that evening (and to bring the only other extant copy of the play, of course).

The steely glint in Beale's eye matches the walls of his study which – did I mention? – are bristling with lethal weapons. Multiplying the contrivances of classic melodramas with a knowing wink, Levin's setting is a positive armoury of antique halberds, daggers and pistols, not to mention several sets of handcuffs, allegedly Houdini's.

At first, the teasing games Levin plays with the old shtick of country-house whodunnits are both clever and funny – almost Stoppardian. When the deceptively naïve Clifford (Jonathan Groff of Glee fame) gets his foot in door, the surprise torques in the storyline produce screams of laughter too.

Yet the real thrill is watching Beale, a truly great actor, find Shakespearean depths in Bruhl. He makes him an Iago in loafers and a showbusiness Macbeth rolled into one, while never missing a comic beat. Beale's combination of physically squat solidity with a mercurial inner life is always fascinating, his emotional intelligence being at once deeply probing and almost diaphanous. He creates ever-shifting layers here, of burning envy, savage aggression, guilt and tenderness.

Even he can't stop Levin's generic clichés and self-referential smirks wearing thin, though. Estelle Parsons, as the Bruhls' psychic neighbour, is a hammy bore, and the closing plot twists are excruciatingly naff. Ouch. Warchus has, characteristically, reckoned on gaining extra credit for making a superficially upmarket, but actually B-rate play look great. But he can't pull that trick off this time.

After his lauded epic Angels in America, Tony Kushner's talent seems to have dwindled lamentably. The Tricycle's latest cycle of plays – an import from Berkeley Rep and Minneapolis's Guthrie Theater – consists of five shorts, collectively entitled Tiny Kushner. Unfortunately, these combine politically sharp ideas with tiresome surreal scenarios and feeble humour.

For sure, Kushner's writing remains boldly idiosyncratic, obsessively working historical figures into offbeat fantasies. A mini-lecture, given by a morally dubious Laura Bush (Kate Eifrig) to ghost-children killed in the Iraq war, is absorbing then prolix. A posthumous meeting, on the moon, between a sour Albanian ex-royal (Eifrig again) and a grinning showgirl (Valeri Mudek) satirises old Europe and madly upbeat American fabulists, but it's irritatingly silly, with musical interludes.

In one of two analysis-obsessed shrink plays, Nixon's Jewish therapist subconsciously treats him as Hitler. Then there's a mock-documentary about cops evading tax, claiming they're not citizens: America's creed of individualism turned criminally selfish. Director Tony Taccone's monochrome set – plastered with bits of text, writ large – looks scrappy and drab. The cast all have their moments, but Kushner's characters are ultimately mouthpieces, spelling out his big ideas.

Finally, Bedlam promises to be crazy fun over at the Globe. Nell Leyshon's new play, set in the 18th-century and revolving around the notorious titular asylum, is boisterously disorderly. Chamber pots are jovially emptied over the audience, while Ella Smith's Phyllis, a shameless harlot, offers punters a grope of her bloomers and her mountainous embonpoint. On stage, ragged beggars mill around, swilling gin and chorusing ballads. Bedlam's unethical Dr Carew (Jason Baughan) is going to the dogs too, drunkenly leering at his new patient, a raving mad beauty called May (Rose Leslie).

Having done her historical research, Leyshon pens some lively period language, poetic as well as bawdy. She is also clearly alert to social and medical progress – or the shocking lack of it – including ghastly procedures with leeches, pin-down techniques, and lethally psychotic cellmates.

Unfortunately, her proliferating storylines are a shambles and some of the acting in Jessica Swale's production is little more than rudimentary. As the foolish and bad poet Laurence, who pays his penny to gawp at the loons, Sam Crane offers only lame clowning, tripping unconvincingly over tin buckets. His attempted rape of May should be far nastier. Daon Broni stands out as her sweetheart and rescuer, and some of the folk songs are lovely, as are the costumes' damson-coloured velvets and apple-green silks. Beyond that, though, just rough and ready.

'Deathtrap' (0844 482 5140) to 22 Jan 2011; 'Tiny Kushner' (020-7328 1000) to 25 Sep; 'Bedlam' (020-7401 9919) to 1 Oct

Next week

Kate is embedded in the National's new political thriller Blood and Gifts.