August: Osage County, NT Lyttelton, London<br>Wig Out!, Royal Court Downstairs, London<br>Tombstone tales and Boothill Ballads, Arcola, London

A family saga by US dramatist Tracy Letts deserves to join the roll call of classic American plays

Nearly 20 years have passed since Chicago's world-renowned troupe, Steppenwolf, last visited our National Theatre. Now they're back, bringing their enthralling tragicomic domestic drama, August: Osage County by Tracy Letts, a Broadway hit which has won multiple Tony Awards and this year's Pulitzer Prize.

Those who recall Letts's past chamber plays, Killer Joe and Bug, may well be expecting another visceral night cooped up with substance-abusing trailer trash in some blood-spattered caravan or roach-infested motel. It is quite a relief to find that this dramatist has moved up the property ladder as well as impressively matured.

In director Anna D Shapiro's staging, the Westons' family home in rural Oklahoma looks like a pretty doll's house: three storeys of lamp-lit rooms, with pointed gables. It appears cosy, yet the skeletal rafters hint at bleakness – pale as bones against the darkness – so in this respect we are still on Letts's old terrain.

The patriarch, Beverly (Chelcie Ross) – a 1960s poet whose writing dried up long ago – is an old soak, quietly nursing a double whiskey as he interviews the prospective Native American home help. His wife, Deanna Dunagan's Violet reels in, still gamine yet wizened. Slurring her words and lurching around in her silk dressing-gown, she is half-crazy on a cocktail of pills and fizzing with insecure spitefulness.

Next thing you know, some days have passed and Beverly has disappeared, apparently having drowned himself in a nearby lake. Thereafter, August turns into a family reunion and dysfunctional meltdown par excellence, as the Westons' three daughters return to the homestead. Accompanied by their variously wayward and long-suffering partners, they fall straight into Violet's lacerating clutches.

Maybe Letts invites comparisons, a tad too obviously, with other canonical greats: Eugene O'Neill, Tennessee Williams, Edward Albee. But what's really joyous is his emergent Chekhovian talent for weaving a broad tapestry, depicting a whole extended household. He combines that with pin-sharp detailing which rings painfully true. Amy Morton's Barbara is unforgettable, howling with grief, then distractedly brushing her hair.

The characters develop surreptitiously, and some of the plot twists pull the rug from under you. The mood swings in this piece are extraordinary too, with vitriol and chilling sleaziness sharing the stage with eloquent dry wit and near-farcical débâcle.

I found Dunagan's Tony-winning tour de force a fraction hammy, sentimentally milking Violet's closing moments of despair. The comedy briefly turns clumsy too, when a physical brawl breaks out. Letts's grandiose intimation that this is all a metaphor for the United States today is not persuasive either. But these are minor cavils: this play fully deserves to join the roll call of classic American plays. What's more, Steppenwolf's ensemble work is superlative. Rondi Reed, as brash Aunt Mattie, is explosively funny yet vulnerable; Jeff Perry is wonderfully lived-in and three-dimensional as Barbara's cheating yet still caring ex, and Morton's emotional breakdown is quietly devastating.

Another US dramatist, the fast-rising Tarell Alvin McCraney, has just received the Evening Standard award for Most Promising Playwright. It's unfortunate timing. In spite of that "fast-rising" tag, his scripts, in truth, are getting weaker. McCraney's British debut, The Brothers Size, was electrifyingly intense: a sibling tussle in impoverished Louisiana. That was recently followed by In the Red and Brown Water: a doomed romance, splashily presented in a huge pool at the Young Vic, but narratively skimped, with too many characters undeveloped.

These shortcomings tiresomely resurface in Wig Out!, though for his fanfared Royal Court premiere, McCraney has shifted to the big city and the spangled underground scene of African-American and Latino drag queens.

Wig Out! zooms in on a competitive strut-your-stuff talent competition between rival gay clans or "houses" (of the sort documented in Paris Is Burning in the 1990s). Director Dominic Cooke has reconfigured the main house for the nonce, stretching the stage into a long gleaming catwalk. Kevin Harvey, as the mournfully ageing "house mother", is splendiferously magnetic and droll, slinking around in white stilettos and a glossy bob, with a quivering bass voice. Danny Sapani has predatory menace as the butch "house father", moving in on the easy-going new sweetheart of the younger transvestite, Nina.

But no number of flaring disco lights can blind you to the glaring omission. There's only a sketchy play here, barely enough to wrap round the central "ballroom" scenes of funky dancing and dolled-up lip-synching. McCraney's recurrent stylish trick of having the characters speak one another's stage directions has already worn thin. Often the dialogue is so choppy, in an attempt to be snazzy, that it is completely uninvolving. Splicing street talk with folkloric archaisms is merely irritating. Why include three Fates – re-envisaged as silver-clad hip-hop gals Fate, Fay and Faith – when they've no impact on the plot at all? Instead, go see La Cage aux Folles, with Douglas Hodge adorable in drag, or wait for Priscilla, Queen of the Desert: the Musical, coming soon to London's West End.

Alas, Tombstone Tales and Boothill Ballads also fails to live up to expectations at the Arcola, though these yarns from the Old West may sound like enticingly alternative comic Yuletide fare. The trigger-happy folks of Tombstone, Arizona, are dropping like flies in this jovial "graveyard cabaret". It's been devised as a family show, for over-12s, by the sporadically inspired physical-theatre director Carl Heap (previously acclaimed for his Christmas shows at the BAC). His young cast are full of brio and some can belt out a rousing ditty, music-hall style. We're offered fiddle-playing, shadow puppets and a few wildly macabre moments, including a hanged man who clog dances in his final twitching minute on the gibbet. Lord knows, though, much of the acting is lame and most of these vignettes could, frankly, bite the dust.

'Wig Out' (020-7565 5000) to 10 Jan; 'August: Osage County' (020-7452 3000) to 21 Jan; 'Tombstone Tales' (020-7503 1646) to 20 Dec