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Strange, beautiful, and strangely beautiful, the Stephen Daldry-directed An Inspector Calls, which first debuted in Britain in 1992 and is running at Shakespeare Theatre Company’s Sidney Harman Hall until Dec. 23, could be said to work its way under your skin. A better description, however, would be to say that it sidles up next to you in evening-ware, mentions a mutual friend, makes a few moments of polite conversation, and then, when you look away to refill your drink, you turn back to find it’s wearing a horrifying monster mask and its outfit is covered in blood.

Make no mistake: This play is a freak. A wonderful freak at that, and far freakier than STC gets on an average day — posh West End credentials notwithstanding. It’s a freak from Ian MacNeil’s poison piñata of a set to Stephen Warbeck’s hilariously melodramatic music. You will leave its company shaking, but you will have been glad you met.

The veddy respectable Birling family (Mr., Mrs., and adult son Eric) is celebrating the engagement of daughter Sheila to (the if anything even more established) Gerald Croft one grey evening in 1912 when their domestic bliss is shattered — nay, burned and pillaged — by the arrival and interrogations of one Inspector Goole (pronounced like “ghoul,” and is it ever). A young woman has killed herself, it seems, and there’s blame to be passed around with the cigars and sherry. To reveal much more would be sinful, but Inspector Calls contains two half-mysteries — one immediate and criminal, one later on and far more metaphysical — and at the same time none at all. The offstage victim truly did commit suicide. Make of that what you will, or, better yet, leave it to the pros on stage.

As the taurine captain of industry, Jeff Harmer excels at living Mr. Birling’s sense of privilege inside-out, and, as his coiled spring of a wife, Christine Kavanagh holds the stage with imperious, pitiless poise. A fantastic performance from Lianne Harvey, whose spoiled, beastly Sheila collapses in on herself like a dying star, combines with jolly good work from Andrew Macklin and Hamish Riddle, whose Gerald and Eric, respectively, get increasingly hot under their well-starched collars amid Goole’s goading.

All of these characters are cliches, but the actors are not — don’t sleep on them — and all of their facades crumble quite interestingly. And at the eye of the storm is Liam Brennan’s inspector, a Scottish voice of decency amid the highly self-centered squabble. Brennan has great comedic timing and he clearly relishes holding all the cards while not failing to keep his own close to his chest, playing both man and enigma.

Originally put on in 1945, J.B. Priestley’s script has been deconstructed and then bulked up on thematic steroids. There will be those who focus on its communal, common-good Message — (hat over heart) “We’ve all got to ‘elp each othah in this ‘orrible, wonderful world…” — but the real highlight is the sly, brilliant way the story goes about telling itself.

Again, spoilers must be avoided. Far better to sit back and take it in. It’s weird as all hell, and that’s one of the best thing about it.