Oedipus, NT Olivier, LondonIn the Red and Brown Water, Young Vic, LondonThe White Devil, Menier Chocolate Factory, London

Ralph Fiennes' Oedipus is on top of the world. In director Jonathan Kent's new modern-dress vision of Sophocles' tragedy, Fiennes strides from the gilded portal of his Theban palace. The ground beneath his feet is domed like the curvature of the earth. Shorn-headed, this is a leader exuding aristo-thuggish potency, like a glaring polar bear.

But he is hardly the happy king of all he surveys. His fortunes and the state's are on the slide. The Olivier stage is slowly – and just perceptibly – revolving off-kilter, queasily unstable. In the background, a blighted tree is glimpsed and David Burke, as a ragged old priest emerging from the audience, is blotched with the plague. Heaven knows, the city's banks have probably collapsed too. Of course, Oedipus will ultimately be forced to see that he is an incestuous parricide and the social canker that must be cast out.

I didn't immediately take to this production. For a while, the sloping revolve made me feel seasick and Fiennes' machismo seemed mannered. The arm movements – hands on hips, then knuckles on table, then shoulders buckling – make him look like a string puppet. Maybe this needs to be more obviously stylised in order not to look wooden, especially as he and Alan Howard's blind, mercilessly foreboding Teiresias intone as if they half-think they're in an opera.

However, it soon becomes clear that that's deliberate. The chorus of anxious citizens is an electrifying male-voice choir. Composed by Jonathan Dove, their threnodies are atonal modern opera blended with ululating folksong and urgent hymns. This thrillingly reinstates Ancient Greek tragedy as music-theatre, and Frank McGuinness's new translation is achingly beautiful, with an extraordinary simple eloquence, almost the poetic equivalent of plainsong. Clare Higgins makes it sound effortlessly natural and is a richly complex Jocasta: a sort of ageing Evita in elegant stilettos, yet a burly matriarch too. Her unconsciously maternal love – stroking Fiennes' cheek – slips unnervingly easily into passionate kisses.

His body language is intriguing too. The stiff body harbours an explosive brutality, and he spasmodically rubs his cranium as if some tumour of guilt is invading his consciousness. He also handles McGuinness's verse with beautiful pacing and a bold crescendo of agony. Finally realising what atrocities he has committed – with his mouth agape like a mask of horror – his rasping animal howl seems to last for eternity. Histrionic perhaps, but hair-raising.

If you're of a delicate disposition and, like Samuel Johnson, find gouged-out eyes too terrible to be behold, then beware. Ears do not fare much better in Tarell Alvin McCraney's disappointing second play, In the Red and Brown Water – a Louisiana tragedy manqué.

The young black heroine, Oya, is a scintillating sprinter, but misses her chance to escape a dead-end life and falls for the swaggering bad boy, Ashley Walters' Shango. He is clearly a leader in the field of aural sex. Ony Uhiara's Oya is instantly seduced whenever he fingers her auricular cartilege. Predictably though, he plays fast and loose, she goes semi-crazy, and someone's shell-like gets the Van Gogh treatment.

This follow-up to The Brothers Size, McCraney's debut, has been eagerly awaited, but the Young Vic's new associate director, Walter Meierjohann, unwisely opts for a big splashy concept. The main auditorium has been turned into a lake. This is eye-catching but unmerited. One minor character recounts a nightmare about skeleton folk on the ocean bed, but nobody seems to notice they're living in a paddling pool. I'm afraid Meierjohann – aka Walter Walter Everywhere – merely dilutes McCraney's drama. You don't want to be watching these guys literally "across the pond". Shunting the audience back against the walls has a distancing effect. The folkloric storyline – drawing on Yoruba myths – when so exposed, looks simplistic.

While the central performances are highly commendable, with Walters oozing testosterone and Uhiara capturing the delicacy of lissome adolescence, several cameo roles come across as irritating cartoon stereotypes. The jazz musician Abram Wilson is a damp squib as well, seated at his piano in the puddle, monotonously hitting one note to indicate melancholy. There are glimmers of brilliance in McCraney's poetically stylised Southern talk but the splooshing drowns out some speeches. See the Young Vic's vibrantly compact revival of The Brothers Size, in the Maria Studio, instead.

Finally, the Menier Chocolate Factory in Southwark continues to impress with its revival of The White Devil, assembling a cast that wouldn't shame the RSC. The sharky courtiers in John Webster's revenge tragedy dive in and out in designer Italian suits. The traverse stage is a sliver of a grand Renaissance palazzo. Aidan McArdle is the sleazy Machiavellian, Flamineo, who plays the pander with his own sister, Claire Price's Vittoria, organising her adulterous liaisons with Darrell D'Silva's Duke of Bracciano. With the help of a necromancer, Bracciano then plots the dastardly poisoning of his wife, leading to reprisals by Louis Hilyer's Duke of Florence who disguises himself as a turbaned Moor.

Heaven knows, Webster's poetry is sometimes like a magpie's hoard of gems snaffled from Shakespeare, yet his imagery and cynicism glitter darkly. In Jonathan Munby's production, doubling makes the fantastically convoluted plot even more confusing and everyone's cunning might come into sharper focus – as should Flamineo's kinkiness, plus McArdle doesn't quite live up to his creepy nail varnish. But this is way-above-par fringe fare. Hilyer's rage is fiercely bullish, Christopher Godwin is a mean Pope – gaunt as an El Greco – and Price's Vittoria is an unsettling mix of wantonness and blonde, wide-eyed innocence.

'Oedipus' (020-7452 3000) to 4 Jan; 'In the Red and Brown Water' (020-7922 2922) to 8 Nov; 'The White Devil' (020-7907 7060) to 15 Nov