Meine faire Dame – ein Sprachlabor, Lowland Hall, Ingliston 2008: Macbeth, Lowland Hall, Ingliston A Midsummer Night's Dream (As You Like It), Royal Shakespeare Theatre, Stratford-Upon-Avon

A polylingual 'Pygmalion' and a Polish 'Macbeth' are among plays unleashed from their language

Professor Higgins (Graham Valentine) in Meine faire Dame gives up on Eliza (Judith Schlosser)

Have the tectonic plates surreptitiously shifted? The capital of Scotland was, surely, transported last week to the avant-garde heart of continental Europe, as theatregoers at the Edinburgh International Festival found themselves in the subversive terrain of auteur-directors from Switzerland and Poland. English classics were being radically rewritten in both cases: to blazes with the original texts.

Actually, under director Christoph Marthaler, Theatre Basel is interested in words, to a degree. His production Meine faire Dame – ein Sprachlabor translates as "My Fair Lady – a Language Lab". Staged at Lowland Hall (a hangar, near Edinburgh airport), this is a tongue-in-cheek travesty of Lerner and Lowe's Broadway musical (itself a rejig of George Bernard Shaw's Pygmalion, of course).

Marthaler's setting is a satirically drab school for TEFL classes. Frumps and geeks, in big specs and 1970s-style polyester, sit in audio booths. The multilingual Graham F Valentine – playing a ratty Professor Higgins in tweed suit and mangy wig – fires random phrases at them, tongue-twisting non-sequiturs with the odd line from GBS in the mix. His pupils, including alternative Eliza Doolittles young and old, parrot him, mangle his words, or stare back silently. Later, snippets from The Magic Flute and Wagner's Lohengrin are pasted into the script. The scenario, meanwhile, morphs into a group-therapy session and concert, with songs from Dowland's "Lachrimae" to Wham's "Last Christmas". A repetiteur is at the class grand piano and Frankenstein's monster plays an electric organ.

This absurdist pastiche is not tremendously entertaining, but Marthaler loosely explores themes of transformation, adoration, scorn, salvation and disappointment. As a trained musician, his overlaying of rhythmic talk and fluid, keyboard harmonies can be arresting. Some startling slides between bathos and poignancy arise too, as Meine Faire Dame becomes a portrait of oldsters. Higgins and the aged Eliza wheel around in office chairs, their physical tussles turning into a waltz.

The action is far more gruesome in 2008: Macbeth, a TR Warszawa production in Lowland Hall's large-scale auditorium. Grzegorz Jarzyna's modern-day reworking of Shakespeare's tragedy, in Polish, envisages Western troops turning on each other in the Middle East and is an epic spectacular, with helicopter searchlights and scorching explosions. The play is set in two-storey military outpost where the concrete washroom is soon swimming in blood. Macbeth is a shorn, pallid killing-machine who hacks off Muslims' heads and starts to lose his wits, tempted by whispering Arab women to assassinate his general.

The acting is uneven (not helped by head mikes on the blink), and Jarzyna's surtitles sporadically, clumsily paraphrase Shakespeare. However, his cast sharply convey that savage attacks and sexual kicks are enmeshed in the Macbeths' marriage and in the troops' debauched partying. The bit-part of the doctor becomes electrifying, played as a fiendishly slinky spirit of vengeance. She lounges upstairs with Macbeth as his white-trash wife haunts the laundry below, forever pulling blood-stained sheets from its glinting, steel washing machines.

A Midsummer Night's Dream (As You Like It) heads for Edinburgh International Festival too this week, after opening in Stratford as part the World Shakespeare Festival. Avant-garde but with a winning spit-and-sawdust aesthetic, this is a lab experiment created by Dmitry Krymov, a set designer turned director. His productions spring from his workshops at Moscow's esteemed School of Dramatic Art. The Dmitry Krymov Laboratory is indeed credited, in the programme, with generating a whole new approach, "designers' theatre", though that's a somewhat aggrandising claim.

A Midsummer Night's Dream (As You Like It) won't live up to its subtitle if you're anticipating an epic fusion of Shakespeare's two comic romances. Krymov is only interested in Pyramus and Thisbe, as staged by the Mechanicals. Nevertheless, this 100-minute production grows from an avant-garde teaser, with acrobatic interludes, into something unexpectedly beautiful and dark: a piece of multidisciplinary bricolage with emotional intensity simmering under its playfulness.

At first, it's comedy chaos as Krymov's ensemble – a medley of stage hands, actors, singers, ballerinas, clowns and a scampering Jack Russell – pretend to be behind schedule. They drag scenery down the aisles: an oak tree (which nearly took my eye out) and an uncontrollably spouting fountain. They then stand petrified for ages, while other cast members – playing snooty patrons, seated amongst the audience – make loud remarks about "modern art" and leave their mobiles chirruping.

They are, however, slowly drawn in, as one mechanical steps forward and becomes feverishly impassioned about Pyramus and Thisbe being towering, ancient archetypes. The doomed lovers are brought to life in the form of gigantic puppets made of found junk, old pots and bandages, combining the wobbliness of Bill and Ben with a haunting delicacy. Their emotions are expressed musically, through jazz scatting and mournful ululations. Meanwhile, Krymov strikingly interprets Pyramus's death as a guilt-ridden suicide. The lion's mauling of Thisbe's garments is pointedly played as an allegory of her sweetheart's callousness: the youth who presented her with romantic bouquets turning into a brutal deflowerer.

It's only a taster, but this summer's programming may well create an appetite for more international fare.

'Meine faire Dame – ein Sprachlabor' (0131-473 2000) today; 'AMidsummer Night's Dream (As You Like It)', King's Theatre, Edinburgh (0131-473 2000), 24-26 Aug

Critic's choice

Nicholas Hytner shifts Shakespeare's riches-to-rags saga Timon of Athens to our era of fat-cat bankers and the Occupy movement. Simon Russell Beale shines in the title role at the NT Olivier, London (to 31 Oct). For summer hols fare, see the RSC's exuberantly funny family musical Matilda, adapted from Roald Dahl, at the Cambridge Theatre, London (until 17 Feb).