Damascus, TraverseEngland, Traverse at theFruitmarketDai (Enough), PleasanceEmergence–SEE!, Assembly @ St George's WestThe Table (Stolik), Assembly Aurora Nova

Paul is selling English-language textbooks. He is a Scotsman in contemporary Syria, trying to push through a deal with their Ministry of Education but doing badly. David Greig's new play, Damascus, uses this scenario – unfolding in a hotel lobby – to explore the West's complex relations with the Arab world.

This is surprisingly entertaining as well as bleak in the end. In director Philip Howard's commendable premiere, Paul is an amusingly flailing writer-turned-salesman (played by Paul Higgins). Casually dispatched by his publisher to the volatile Middle East, he is nervous and simultaneously naive about cultural divides.

For starters, he is floundering linguistically, compelled to rely on a distinctly selective translator or use his laughably rusty French. His contact, Alex Elliott's Wasim, is an ex-radical poet-turned-bureaucrat, only interested in laying his colleague, Nathalie Armin's Muna. She is irked by Paul's textbook featuring "user-friendly" multicultural cartoon strips. She demands rewrites although her stance is complicated, partly feminist, partly orthodox Muslim. She and Paul are attracted too, only she stands him up and he goes on a bender with the hotel porter. Both men yearn to change their lives, though if Paul goes through any conversion in Damascus, it's one that leaves him older, wiser and harrowed with guilt.

This piece is indebted to Brian Friel's Translations and brings The History Boys to mind as well, discussing imperfect tenses and states of wishfulness.

I could certainly have done without the foyer pianist, a pretentious choric commentator. Nevertheless, this is a strongly structured and intelligent play, informed by the dramatist's own British Council work in Syria. Crucially, it engages with the big issue of racial misunderstandings and with the pressing question of where we should draw the line, accepting or rejecting the mores of foreign cultures if we fundamentally disagree.

Translation also plays a key role in England. In this site-specific piece by experimentalist Tim Crouch, a man and a woman (Crouch and Hannah Ringham) stand smiling nervously at you, taking it in turns to speak. Occasionally, they lead the audience to another corner of the Fruitmarket Gallery's current art exhibition. They engage in no direct dialogue. It's more as if they are relaying diary entries. Gradually, we piece the story together. There's an adored American boyfriend. He's a globe-trotting art dealer who owns a London loft apartment, but illness threatens this idyll. In the second half, we are somewhere abroad. A heart transplant has averted death and the widow of the donor – who was called Hassam – is being visited, with a gift of thanks. However, we glean through an interpreter that the widow is distraught and furious. She believes Hassam was allowed to die because stacks of money were being paid for the Western patient's private op.

Some will, doubtless, find this duologue too coldly detached and avant-garde. Yet the storytelling is intriguingly slippery. You are transported through time and space, jumping months and continents. There are worrying gaps. The two interlocutors also blur, their personalities at times merging, at times changing. These confusions of identity climactically reflect the ethical and highly emotional issue of who a transplant patient is exactly, if their heart is that of someone else's dear departed. Beyond this, is the question of whether West and East can co-exist in harmony.

In the one-woman play Dai (Enough), the writer-performer Iris Bahr morphs into nearly a dozen characters in a Tel Aviv cafe, simply slipping into different jackets which are hung – like mournful ghosts – over the backs of chairs. Everyone we meet is about to be blown to pieces by a Palestinian suicide bomber.

From the humane old Kibbutznik sustaining hope to the gay German ex-pat, to the ferociously militant Zionist, we are just getting to know each individual when they are ripped away, falling in slow motion. The repeated sound of the deafening explosion is shocking every time. We do not get all sides of the story here. The bomber is given no monologue. Nonetheless, Bahr presents an illuminating group snapshot of a multicultural society, holding diverse political opinions yet all facing the same dangers.

In another solo performance called Emergence-SEE!, a dazzling black American actor/singer/performance poet, Daniel Beaty, makes psychologically explorative use of multiple role-playing. A ghostly slave ship has, surreally, risen out of the Hudson, right by the Statue of Liberty. Most of New York rushes to see it. Beaty plays 40characters, from entertainingly mouthy old junkies to sweet Harlem kids to angry hoodlums, slinky transvestites and an ageing black academic who, having tried to simply escape the ghetto and forget the past, has developed schizophrenia. Beaty's transmogrifications are brilliantly fluid, clear and witty. The piece is, at the last, excessively didactic, but it's a fascinatingly mercurial performance, embodying the notion that a repressed race have conflicting selves inside them.

Finally, The Table (Stolik) – created by the Polish group, Karbido – takes us on an electrifying acoustic journey round the globe. This "piece for four men and a table" is really an inspired DIY concert. They look as if they're sitting around at home, drumming their fingers on the kitchen table or brushing off some crumbs, but this is an intricately amplified piece of furniture. Adding in reverberating wine glasses and ululations, and whispering through cracks in the wood, they move musically round the four points of the compass, from the mystical chimes of the East to the pulsating tropical South to the hard-rock West and wonderful icy echoes up at the North Pole. Superb.

'Damascus' (0131 228 1404) to 26 August; 'England' (0131 228 1404) to 26 August; 'Dai (Enough)' (0131 556 6550) to 27 August; 'Emergence – SEE!' (0131 623 3030) to 27 August; 'The Table' (0131 623 3030) to 27 August

Need to know

David Greig's first play was produced in Glasgow in 1992. In 1990 he co-founded Suspect Culture Theatre Group with Graham Eatough. Greig was born in Edinburgh in 1969 and brought up in Nigeria. He studied drama at Bristol University alongside Simon Pegg. He has been commissioned by the Royal Court, the National Theatre and the Royal Shakespeare Company and is currently Dramaturg of the National Theatre of Scotland. Greig was shortlisted for the TMA Theatre Award for Best New Play in 2005 for his play 'Pyrenees'. He directed 'Blackwatch' which took last year's Edinburgh Festival by storm. At this year's festival, his new play 'Damascus', is the centrepiece of the Fringe programme

Further reading David Greig's 'Plays 1: Europe, The Architect, and The Cosmonaut's Last Message' (Methuen)

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