Pygmalion, Old Vic, London<br />The Good Soul of Szechuan, Young Vic, London<br />The Birthday Party, Lyric, Hammersmith, London

Shaw's classic revels in timeless themes and a talented cast; by contrast a Brecht revival seems didactic and dull

Tim Pigott-Smith's Professor Henry Higgins is holding forth while munching on a sweet. He's sprawled in an armchair and blithely wiping his nose on his tie, like a schoolboy, in Sir Peter Hall's enjoyable production of Pygmalion (transferring from the Bath Theatre Royal). The sharp point of Shaw's social comedy is precisely this: while Eliza Doolittle (Michelle Dockery) lacks breeding and drops all her aitches, the "gentleman" phoneticist who's determined to pass her off as a pukka duchess displays far from impeccable manners himself.

Pigott-Smith captures the shocking rudeness of which the intelligentsia can be guilty. He's the voice of outrageous snobbishness as he scorns the guttersnipe. Using Eliza as his experiment, never thinking of the consequences, he is also the stereotypical scientist – callous and ethically dubious.

However, what this production most clearly brings out is Higgins the confirmed but confused bachelor. Confessing that he really wants a woman like his no-nonsense mater (Barbara Jefford), there's a touch of oral fixation about his habitual sweet-sucking. Moreover, in the final scene, he's hopelessly in denial about finding Eliza attractive, reaching out to touch her but repeatedly backing off. A man in the audience on the night I attended was so frustrated that he shouted out, "Kiss her!", to no avail. Ungraciously treated as a second-class citizen or mere commodity, Eliza walks out like an Ibsen heroine, leaving the professor on the brink of tears. He has learned his lesson too late.

Pigott-Smith perhaps fractionally overplays the physical mannerisms and there could be more teasing sexual chemistry, but Sir Peter's whole cast is commendably strong. Dockery's Eliza, in cockney mode, is refreshingly uncaricatured. She has a touching silent mournfulness too, when she's exquisitely dressed in cream silk gowns but is still being treated like a doormat. Una Stubbs is on good form as the housekeeper, Mrs Pearce, urgently concerned for the girl and secretly fond of Higgins herself. Meanwhile, Tony Haygarth is the most charming Alfred Doolittle I've seen: a merrily shameless, motor-mouthed scrounger with a twinkle in his eye.

It's the Gods who nudge the lowly prostitute, Shen Te, up the social ladder in Bertolt Brecht's The Good Soul of Szechuan. A delegation has been sent from heaven to search for a decent citizen. This is like hunting for a needle in a haystack. Jane Horrocks's Shen Te is the only person kind enough to offer the deities shelter for the night.

Rewarded with sufficient cash to buy a tobacco shop, she then tries to run her business and be charitable to the poor – swiftly becoming nicknamed the Angel of the Slums. Nevertheless in Brecht's cynical parable – penned in the early 1940s, before the Chinese communists gained control and, of course, not foreseeing this week's tragic earthquake – Szechuan is envisaged as a realm of charmless scavengers, scamming at the bottom of the capitalist pile.

Shen Te is ripped off by squatters and a money-grabbing sweetheart. So just to survive, she is compelled to adopt a hard-nosed alter ego, slipping into a pin-stripe suit and trilby and pretending to be her tough male cousin, Shui Ta. Think caring sharing liberal-turns-mafia geezer. She ends up dealing heroin in David Harrower's new but not stringently updated translation. Richard Jones's staging gets off to an enticing start. The Young Vic's auditorium had been transformed into an epic warehouse market: high plywood walls, glass booths and bright advertising banners. Visually, this has a stark stylish beauty with dream-like touches: when the bureaucratic Gods start ringing on doorbells, scowling faces pop out of tall steel lockers, and heroin addicts drift around with paper bags on their heads branded with smiley faces.

This styling does not, however, generate a sense of genuine squalor, nor can it conceal that Brecht's folktale becomes dull, didactic yet not illuminating. With paper-thin characters, the cast rarely get a chance to be engaging either, though Adam Gillen stands out playing the penniless water-seller as a frantic simpleton. Jane Horrocks is disappointing in the title role: arrestingly gaunt but tiresomely baby-voiced as Shen Te. Turning into Shui Ta, she's not thrillingly different. As for the musical numbers, David Sawer's arrangements are edgily atonal but wan.

Finally, David Farr's new Lyric Hammersmith production of Harold Pinter's The Birthday Party marks this modern classic's 50th anniversary. The London premiere, at this address, was notoriously panned, except by one critic, Harold Hobson, who recognised the playwright's extraordinary talent to disturb.

That power has not diminished. What's riveting about this seedy boarding-house drama is how it begins as a comedy of banality – with ludicrously dreary circling conversations about cornflakes – before you're sucked into a weird nightmare where unexplained interrogators come to torment the scraggy lodger, Stanley, who is teetering on the edge of a mental breakdown.

It must be said that Nicholas Woodeson sometimes lets the predatory menace slacken as Goldberg, and Justin Salinger, playing Stanley, hams up a few dramatic moments, darting like a ferret or freezing on the spot – almost physical-theatre style. However, Farr brings out how this darkening comedy looks back to Pinter's early comic sketches and forward to his more directly political plays. Sheila Hancock is also outstanding as the landlady, Meg, making her slightly backward, so she's a seedy old baggage in curlers but with the sweet naivety of a child.

'Pygmalion' (0870-060 6628) to 2 August; 'The Good Soul of Szechuan' (020-7922 2922) to 21 June; 'The Birthday Party' (0870-050 0511) to 24 May