The Master and Margarita, Barbican, London Sweeney Todd, Adelphi, London Filumena, Almedia, London

Demons do not exist any more than gods do, said Sigmund Freud. Ivan Bezdomny would beg to differ in Mikhail Bulgakov's great, darkly surreal and satirical novel The Master and Margarita – newly staged by Complicite's Simon McBurney (drawing on Edward Kemp's adaptation). Bezdomny has seen Satan sloping around Stalin's Moscow with a gang of fiends, including Behemoth – a black cat who stands as high as a man on his hind legs, and can talk.

It's a spring evening: shafts of fading light; the rumble of passing trams. Richard Katz's Bezdomny, a writer, is sitting on a park bench with his editor, Mikhail Berlioz (Clive Mendus). A Soviet apparatchik promoting atheism, Berlioz is reminding Ivan that the Christ story is a complete myth when a preposterously macabre stranger sidles up in a beret, dark glasses and leather gloves (some distant relative of Dr Strangelove, surely). There's a glint of iron teeth as this self-styled expert in black magic – aka Woland – insouciantly predicts that Berlioz will be decapitated, then starts relating how he himself attended Jesus's trial, hovering around Pontius Pilate.

Scurrying off to report Woland to the authorities, as a suspected madman or foreign spy, Berlioz slips under a tram – neck severed. Then Ivan, gibbering accusations, is slammed in a lunatic asylum, along with another condemned writer, The Master (a pale, feverish Paul Rhys). Woland and his cronies, meanwhile, commandeer Berlioz's flat, "disappear" anyone troublesome, gull the masses with magic, and invite the Master's ex-lover, Sinead Matthews's Margarita, to their Walpurgis Night ball.

McBurney's multimedia staging has fantastic moments, orchestrating amplified sound, physical theatre, live camerawork, and swirling projections. Margarita's hallucinatory flight, when she leaps like an avenging witch out of her apartment window, is breathtaking and technologically brilliant. With her body smeared with a burning, blue diabolical ointment and perhaps in her death throes, Matthews is seen writhing madly on the stage while, simultaneously, she's projected on a window ledge high above, plunging headlong from it, seemingly for ever, in blurred streaks of light.

At this early stage in the run, other scenes feel slightly slack, over-busy with less brilliant ideas, and puzzlingly diffuse rather than dramatically concentrated. McBurney's recent ENO staging of the Bulgakov/Raskatov opera A Dog's Heart was tighter, the diabolical dog scarier than Blind Summit's scraggy cat puppet here.

Still, it's inevitably going to be hard to nail exactly how the storyline of Pilate, Woland and Christ overlaps with Stalin's regime, Berlioz, Bezdomny, The Master, or the punitively censored Bulgakov himself. Playing safe necessitated tangential allegories. Bulgakov's novel is like a vast, labyrinthine dream. I get the feeling McBurney is still grappling with this leviathan, trying not to crush it. Work in progress.

Moving on swiftly to the demon barber of Fleet Street, Sondheim's dark musical Sweeney Todd, starring Michael Ball and Imelda Staunton, is set in a sooty inferno, scarred by blades of light. Iron stairs spiral down to the bowels of Mrs Lovett's pie shop, where an oven belches smoke and the gore-splattered corpses pile up. The serial killer stands on high, his cut-throat razor flashing silver, as he swears to avenge the injustices he has suffered.

Maybe director Jonathan Kent's spotlit tableaux border on the hammy in this transfer from Chichester. The 1930s costumes don't fit the Victorian references (Beadles and Botany Bay). And Sweeney's long-lost daughter (Lucy May Barker) seems a bland goody-goody. Essentially, though, Sondheim's score still thrills, evoking folk ballads with a jagged edginess. Ball is frighteningly morose, this typically chirpy performer transmogrified into a hulking psychopath, with a greasy forelock and ghoulishly pallid face. Though her singing voice isn't as storming as his, Staunton's Lovett is far from outshone, bustling around with terrific comic timing. She is also genuinely sweet on Sweeney, though a merciless profiteer.

In the 1940s Neapolitan comedy Filumena, by Eduardo De Filippo, Samantha Spiro is the titular heroine who pretends she's dying to trick Clive Wood's Domenico into finally marrying her. He first met her in a slum brothel, and, having become a rich man, set her up as his kept woman years ago.

Laughing triumphantly, she says that from now on he'll be playing by her rules. He furiously wriggles out through a legal loophole, reviling her as a whore. Then she reveals, to his amazement, that she has three grown sons, one his own flesh and blood. Since he can't work out which that is, he'll have to do the decent thing after all, remarry her and be a loving, even-handed father to each of them.

De Filippo was himself the illegitimate son of a promiscuous rover. Filumena's speech, defending the uncomfortable moral choices she has faced as an underdog, feels like a startling, radical shift towards feminist docudrama, and this playwright is famous for having written in the dialect of Naples. That is, alas, hardly reflected in Tanya Ronder's clunky translation, or Spiro and Wood's RP accents. Michael Attenborough's production is picturesque – unfolding in the courtyard of Wood's villa, complete with orange tree – but the humour often seems feebly meandering.

'The Master and Margarita' (0845 120 7511) to 7 Apr; 'Sweeney Todd' (0844 811 0053) to 22 Sep. 'Filumena' (020-7359 4404) to 13 May

Theatre choice

Moon on a Rainbow Shawl, Errol John's tragicomedy of shanty-renting neighbours in 1940s Trinidad, is beautifully acted at the NT Cottesloe, London (to 9 Jun). Also in London, Ben Chaplin is superb in Richard Nelson's Farewell to the Theatre, a biodrama about Edwardian actor-manager Harley Granville-Barker, at Hampstead Theatre (to 7 Apr).