Vanya and Sonia are middle-aged siblings who never managed to launch individual lives. After nursing their parents through final illnesses, they’re growing old in the family home, having the same conversations and arguments every day and resenting their absent sister’s success.

If this sounds, vaguely and a bit alarmingly, like something by 19th-century Russian author Anton Chekhov, you can relax. It’s actually the setup for Christopher Durang’s antic comedy Vanya and Sonia and Masha and Spike, which won the Tony Award for Best Play in 2013.

At the Martha’s Vineyard Playhouse through August 3, director MJ Bruder Munafo’s lively, assured production makes the most of Mr. Durang’s breakneck script, with a cast that’s more than equal to the challenge of fully inhabiting six quirky roles while representing more than a dozen characters in all.

Still in their nightclothes, Vanya (Brandon Whitehead) and Sonia (Cate Damon) have barely started their morning routine—drinking coffee, airing resentments and disregarding dire predictions from Cassandra, the cleaning lady—when big sister Masha blasts back into their lives.

Stephan Amenta, Shelagh Hackett and Cate Damon — MJ Bruder Munafo

An aging movie star, armored in glamour but headed for grandmother roles, Masha is fending off time with the help of paramour/protege Spike, a vain young hunk prone to taking off his clothes in company.

Some of the funniest moments in the playhouse production are Mr. Whitehead’s wordless reactions while Vanya, gay and helplessly vamped, watches Spike flex and preen in his direction.

As Masha, sweeping back into her siblings’ lives, Shelagh Hackett exemplifies the drama queen who plans a group costume for a fancy-dress party with herself as Snow White, her date as Prince Charming and her siblings as dwarves. Vanya accepts his fate, only insisting he be Doc instead of Grumpy. But Sonia refuses to don Dopey’s tunic and Phrygian cap, instead making a rare foray to buy a costume that will let her become the Evil Queen—as played, she imagines, by Maggie Smith, the actress who won an Oscar for playing an Oscar-nominated actress in California Suite.

Cate Damon’s performance as Sonia is another riveting turn in an evening full of surprises.

Ellie Brelis, who has appeared in several Shakespeare productions at the playhouse, shows an easy grasp of comedy as Nina, the starstruck ingenue who wanders over from next door. Fangirling with all her might, Nina happily wears the Dopey costume and, when Vanya agrees to have a reading of his avant-garde play about the weather, throws herself into the helium-voiced role of a lonely molecule in the aftermath of the Earth’s destruction.

The play’s most consistently strange and hilarious character is Cassandra, played with demented vigor by Mona Hennessy as she strides around the set—designed by artist and actor Sean Roach—making pronouncements like “I see disaster ahead for all of you! Lunch in about 20 minutes.”

Mr. Durang, who has clearly read his Algonquin Round Table writers, sets Vanya and Sonia and Masha and Spike in Bucks County, Pa., where several of the witty group’s core members had country homes in the mid-20th century. The play’s costume party takes place, between acts, at the home formerly owned by Dorothy Parker.

The role of Spike in this production is played by Stephen Amenta, who in June appeared as a teenaged S. J. Perelman in the playhouse reading of Marc Kirkeby’s Sid & Howard.

After Vanya and Sonia and Masha and Spike closes August 3, the season’s final main stage production is the musical revue Low Down Dirty Blues (August 10-Sept. 7).

At the Tisbury Amphitheater, the playhouse production of Shakespeare’s The Winter’s Tale continues Thursday through Sunday at 5 p.m. through Aug. 11.

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