Relocated, Royal Court Upstairs, London<br/>...Sisters, Gate, London<br/>2,000 Feet Away, Bush Theatre, London

A truly unsettling journey into the dark realm of domestic atrocities

Anthony Neilson writes frighteningly dark plays. He occasionally lightens up with a psychedelic comedy, but with his self-directed new piece, Relocated, he's back exploring the sinister depths of a twisted mind – or multiple twisted minds.

It's almost pitch black in the realm inhabited by his weirdly proliferating characters. Staring into the murk – through a gauze, like a half-silvered mirror – you initially make out a lone woman (Jan Pearson) Hoovering in a nightmarish sepulchral cellar. Suddenly she collapses – dead or just having a seizure? This is the first in a sequence of disorienting, possibly deranged and hallucinatory scenes, glimpsed between blackouts.

An eerie pale light returns. The woman is standing again and a burly man (Stuart McQuarrie) steps from the shadows, asking questions and telling her to move on. When he vanishes, a second woman (Nicola Walker) pops up: a new neighbour, smiling, scarily braying. She holds out a child's painting left behind, she says, by the former occupant. Darkness again, then these two women have switched places, changed names. There's a third in this chain too (Frances Grey). All three are classroom assistants, maybe in different places or times, but each is haunted by ghostly children's cries.

Their partners behave like steady ordinary guys: Phil McKee as a teasing Scottish teacher and Stuart McQuarrie now trolling around in his dressing-gown. But is anyone what they seem? Conversations at the kitchen table slip into chilling insanity and uncertainty. McQuarrie mentions that he's left the water in the bath for the kids. There's a pause. What kids? asks Grey.

It slowly becomes clear that Neilson's female characters are obsessed by – or have become directly entangled in – horrible cases of girls being incarcerated or killed. There are allusions – albeit fictionalised – to those domestic dungeons in Austria and the tragic Soham murders. The visions on stage grow increasingly gruesome too, while the acting remains superbly understated. This is one of the creepiest plays I've seen.

Characteristically, Neilson pushes the bounds of decency, turning gruesome news stories into contemporary gothic horror. It's not morally comfortable, yet that is surely the point. Relocated taps into the profound permeating terror such atrocities generate, as well as raising disturbing questions about the morbid fascination they exert.

Yet Neilson has not managed to work elements from the ongoing Josef Fritzl case into a fully matured drama, creating a weak ending. At its most powerful, though, this drama touches on very immediate fears while conjuring up almost mythic horrors: most unforgettably, a ghoulish woman with monstrous hands trailing below her knees, and a rag doll – the size of a 10-year-old – scrabbling in a corner, her face flashing round at you like a howling Greek mask.

The experimental deviser-director Chris Goode has, meanwhile, turned his hand to radically adapting a classic: Chekhov's Three Sisters. The result is disappointingly reductive. In ...Sisters, five young actresses and one chap in a petticoat give patchy performances, endlessly swapping hats and sharing a dozen roles. Anyone who doesn't know the original well will be confounded. That said, a tiresome evening eventually reveals its purpose. Goode is really exploring the choric or near-orchestral nature of Chekhovian conversations where speeches are like lines on a stave, not so much responding but almost running in parallel, sharing leitmotifs.

As tempers fray in act three, Goode pushes the experiment till everyone talks over each other in a symphonic hubbub; then act four's farewells quieten into a tableau – like a last snapshot, as everyone gazes into the future – with thoughts drifting from one person's lips to the next, like leaves carried on the breeze.

Lastly, Joseph Fiennes proves to be a sorry case of star miscasting in 2,000 Feet Away. Anthony Weigh's debut play is set in small-town evangelical Iowa where the deputy sheriff is having to evict a plague of paedophiles. Weigh has a commendable ear for vernacular chat, but his storyline is muddy, as is any moral point he's trying to make. This is not helped by Josie Rourke's lack of directorial acumen.

As the deputy, Fiennes strikes a series of clichéd cowboy-movie poses while failing to pick up on intimations that his character may be sullied with lewd thoughts about underage girls. Veering between tolerance and fits of rage, he is surely more messed up than this tepid actor conveys. He's definitely supposed to be a bit of a loser: no girlfriend and forever stuffing his face with junk food on the job. Risibly failing to get into character, Fiennes nibbles on peanuts one at a time.

'Relocated' (020-7565 5000) to 5 July; '...Sisters' (020-7229 0706) to 5 July; '2,000 Feet Away' (020-7610 4224) to 12 July