Mademoiselle Julie, Barbican, London Love and Information, Royal Court, London Three Sisters, Young Vic, London

The country house has been modernised. Rather than a 19th-century pile, the Count's manor is minimalist – sliding sheet-glass and white walls – in Strindberg's Miss Julie, or Mademoiselle Julie as it's called in this French production (with English surtitles), starring Juliette Binoche.

While her pater is away, Binoche's aristocratic Julie is playing around with his valet, Jean (Nicolas Bouchard). The other servants have the run of the place on this Midsummer's Eve, too, in Frédéric Fisbach's sleek, sensual production. Household staff are seen upstage, boozing and dancing to Frankie Valli ("Beggin'") and Blondie ("I Can't Control Myself"). Some slip into the lounge to canoodle.

The fact that Julie and Jean's sexual liaison is supposed to be a potentially suicide-inducing transgression of class boundaries might not seem to fit a 21st-century setting. Yet, this director makes almost everything plausible.

Binoche's Julie is complicated, blowing hot and cold. She looks like a tousled It girl. And she's an inveterate snob in her gold-sequinned dress; mentally fragile as well – sobbing like a little girl when rejected.

Bouchaud may have his eye on Julie's wealth, but his Jean seems far more loving than most productions allow. Tenderness, desire and desperation are all here, the duo's one-night stand staged as glimpsed moments punctuated by blackouts. A sense of magnified intimacy is created as the actors perform behind glass, their voices amplified.

It's less convincing when the production switches into hallucinatory surrealism, the masked dancers turning into prowling beasts. Nonetheless, Binoche is strongly supported, indeed sometimes outshone, by Bouchaud and by Bé*édicte Cerutti as the third player in the love triangle, Jean's uncowed fiancée.

In Love and Information – Caryl Churchill's radically fragmentary new play, directed by James Macdonald – you see myriad characters as if by flashes of lightning, some 50 snapshots swiftly plunging into darkness. The scenes are disconnected but with some teasing, possible links emerge. There are lovers wanting to know everything or wishing they hadn't asked; jobbing torturers, taking a fag break, not bothered if what they extract is the truth; cases of neurological malfunctions; a delusional schizophrenic; a rational cynic unable to understand another's religious convictions; a lefty intellectual claiming she "always knew" Tony Blair's warmongering excuse was "all made up".

By the end, I didn't feel I had learnt much. Indeed, anyone who has read V S Ramachandran or Oliver Sacks will recognise the neurological case histories reduced, here, to little more than sound bites. But to complain that Love and Information lacks depth is to miss the point. Churchill is ruminating – satirically and movingly, too – on how little most people know of each other or themselves. As it progresses, the piece also touches on big issues, from genetics to free will. Mini-dialogues are fleshed out by the cast with such pin-sharp naturalism that you are able to read a character in a millisecond. Designer Miriam Buether and the Royal Court's technical crew deserve an award, to boot, for the miraculous scene changes, where double beds and lawns and café tables materialise with the ease of a dream.

Perhaps Chekhov was also in the back of Churchill's mind. Hovering between mournfulness and hope, his Three Sisters ends with lovers lost and Olga trying to console her bereft siblings. Yearning to comprehend why we live and suffer, she famously repeats the line "If only we knew".

In the Young Vic's new modern-dress production – staged by Australia's Benedict Andrews with a largely British cast – Mariah Gale utters Olga's last words like an ecstatic prayer, while Michael Feast's jaded Dr Chebutykin mutters "Who cares? Who even cares?" as he sits thumbing through a newspaper.

Chekhov aficionados will find themselves on less familiar terrain with some of the dialogue elsewhere in this adaptation. Feast's Chebutykin alludes to an article he has read about robot technology replacing hair follicles, while William Houston's Colonel Vershinin suggests that happiness is "a marketing ploy", and Vanessa Kirby's Masha chips in, "Didn't someone once say, 'If the world didn't suck, we'd fall off'?"

I have enjoyed many reworkings of this play. However, Andrews's strikes me as clunking, though it has a look of stylish trendiness, with a vast bare stage overhung by a glowing light box, like a grey sky.

Rather than seeming timeless and universal, this 1904 classic, set in a Russian garrison town, seems to have been transported to a historical nowhereville. I found it hard to believe – even if the Prozorovs overestimate their talents – that Andrey's sisters could ever have imagined their brother a professor in the making, as actor Danny Kirrane slobs around in sweatpants, with naked wobbling belly. Many of the cast appear to have been left to deliver their speeches in a flat, wooden tone. Others rise above this, including Houston, and Sam Troughton as the bright young soldier, Tuzenbach. He philosophises with enthusiasm and his unrequited love for Gala Gordon's Irina makes this Three Sisters, ultimately, his tragedy.

'Mademoiselle Julie' (0845 120 7511) to 29 Sep; 'Love and Information' (020-7565 5000) to 13 Oct; 'Three Sisters' (020-7922 2922) to 3 Nov

Jonathan Pryce is on storming form, brilliantly naturalistic and psychologically complex, in Michael Attenborough’s staging of King Lear at the Almeida, London (to 3 Nov). In a short West End run of the acclaimed adaptation of Michael Morpurgo’s Private Peaceful, at London’s Haymarket Theatre Royal (to 29 Sep), Paul Chequer and fast-rising star Mark Quartley share the title role.