Of Shakespeare’s comic progeny, Twelfth Night is the melancholy baby, and director Steven Maler rocks it deftly. His staging, on Boston Common, is ephemeral, elegant, and, when Sir Toby Belch and his questionable crew hold sway, drop-dead funny. In the urban outdoor venue, where planes and street noise (with or without sirens) necessitate amplification, some of the play’s luxurious poetry — particularly Viola’s — blares. Other than that, CSC’s sixth and best offering of free Shakespeare in the park proves you can indeed look a gift horse in the mouth. And in this case, you’ll find it has both smile and bite.

The production is heady with humorous invention, primarily in the scenes in Sir Toby’s lair, which is stocked with an icebox full of beer and a jukebox that Maria likes to bump into "on" mode with her ass. But Twelfth Night’s plot crawls as much with unrequited love as with comic insurrection. Duke Orsino is besotted by the lady Olivia, who shuns him for an orgy of mourning. The shipwrecked Viola (who makes her entrance through a door in the ocean) dons man’s guise to serve Orsino, but that just sets up a sexually ambivalent triangle in which Viola dotes on her master, who sends her to woo Olivia, who falls hard for the page. Then there’s Olivia’s puritanical steward, Malvolio, whose dour self-regard is trumped only by his secret yearning for his mistress and her social position — which he’s tricked by Sir Toby and cronies into acknowledging. That results in a comeuppance that turns from just deserts to downright cruelty. The show on the Common makes the play’s comedy, even the more arcane bits, as zany as I Love Lucy, but with a Martin McDonagh edge. At the same time there remains among the lovers, even given the neat trick of Viola’s androgyny, the sense of troubled wonder that informs that stolen ditty from Merchant.

According to director Maler, he located his Twelfth Night in the blink of the "American Camelot," that intersection of the 1950s, with its Eisenhower-era repression, and the more sexually greased ’60s to come. In fact, that idea seems most pertinent to the score, which mixes jazz with early, blues-influenced rock, including music by Ornette Coleman and James Brown. The Bard’s own song lyrics are supplied with smoky-jazzy tunes composed by sound designer J Hagenbuckle and LeBow and played by the latter on the electric keyboard he wears slung over his shoulder like a guitar. The music is very effective and, when it crosses into the absurd improvisational riffs with which the party-animal contingent surrounding Sir Toby infuriate Malvolio, hilarious.

But the production’s look canopies a wider stretch of time and place, with influences ranging from India to Gene Simmons. Dodge’s setting is romantic yet spare, with a ribbon of a spiral stair set against the sea and Olivia’s digs decorated by phallic cactuses encased in plexiglass boxes. Costume designer Gail Astrid Buckley provides some slinky old-movie duds for Siobhan Juanita Brown’s Olivia and blows up a whirlwind of comedy for the comic-subplot co-conspirators, from the lime-green and turquoise suits with gold neck chains for John Kuntz’s squeaky Sir Andrew Aguecheek to the ’60s sexy-wench wear for Karen MacDonald’s Southern Erin Brockovich of a Maria. And believe me, you have never seen Malvolio "cross-gartered" like this, Thomas Derrah’s thighs protruding from little yellow underpants and his whole body criss-crossed in leather and chains.

Perhaps inspired by their get-ups, the comic performers prove so inspired that the play’s gender-bent lovers, though adequately performed, pale in comparison. Brown is a dignified Olivia who gradually turns girlish, indulging in a giddy giggle fest with serving woman Maria and eventually going after Viola, disguised as Cesario, like Helena-as-spaniel in A Midsummer Night’s Dream. She also manages a round tone that serves the language well. D’metrius Conley-Williams is a voluptuous if not terribly interesting Orsino, in whom there is an undercurrent of sexual attraction to his page, whom he tenderly tweaks and clasps even as he calls him/her "boy." And there is a heightened moment in which the two, exotically clad master and white-baggy-suited servant, succumbing to the spell of a plinking piano, almost kiss. As for Cheryl Gaysunas’s Viola, she’s adorable if unpoetical — a studiedly cocky pretend-youth, hands in pockets and heart in throat, always fearful of discovery. And feigning inability to lift the hunk of a sword she’s provided for her duel with Kuntz’s Sir Andrew, she proves an able physical comedian.

In that department, of course, she faces the big guns — most of them on loan from the arsenal of the American Repertory Theatre. ART stalwart Derrah is a fluty baldpate of a Malvolio, less Puritan than fascist, stiffly following his mourning mistress with a tiny replica of the cacti that seem her prickly coat of arms. He wears a little notebook for tattling as if it were a medallion, and he affects a pompous delivery in which most of the consonants become extra syllables. "Practicing behavior to his own shadow," he strikes poses worthy of Rodin; duped by Sir Toby, Maria, and the gang into believing himself Olivia’s secret love, he survives an outrageous onslaught of exaggerated eavesdropping without breaking concentration. He caps it with a dash up the spiral stair, right over the skulking bodies of his nemeses! Yet the Malvolio unleashed by this silliness, something between a rocker and a satyr, mixes pomposity with vulgarity. And the abused Malvolio, imprisoned in a glass cube smeared the color of his stockings, is truly pitiable. It is one of the production’s marked successes that it retains the discomforting cruelty waiting at the end of what is here a wildly broad comic path.

Among Malvolio’s torturers, who take more liberties with Shakespeare’s routines than they do with the steward, an almost unrecognizable Richard McElvain plays Sir Toby as a grizzled biker, wringing laughs from his growly bravado and calypso moves, yet imbuing the cadging, drunken old funster with a sinister streak. MacDonald, apart from mincing pricelessly about on her tiny high heels and inventing a laugh that hovers between cackle and hyperventilation, turns Maria into a cross between a twanging biker broad and a smart personal assistant. The business she and Maler have hatched out of the line "here comes the trout that must be caught with tickling" is as sublimely ridiculous as it is literal. Tagging at the heels of Toby and Maria (when he isn’t leaping into the former’s arms), Kuntz’s Sir Andrew is like a day-glo Bertie Wooster, absurd yet touching. Even Jonno Roberts’s punk-platinum-tressed Fabian is a presence to be reckoned with.

But the presiding spirit of this Twelfth Night, playing it on and off like a burnt-out lounge pianist, is LeBow’s dying comic of a Feste. His original ditties range from the pointedly perky ("What is love? ’Tis not hereafter") to the melancholic (the closing number, "When that I was and a little tiny boy," has the gruff, talk-sung poignancy of Elvis’s "Are You Lonesome Tonight?"). Not only does LeBow put those who can’t walk and chew gum to shame by acting and singing while playing a piano strapped to his chest, he also brings real muscle to the Clown, meeting Malvolio’s threat of revenge, for example, with a vengeance of his own. Moreover, his tired jokes, capped by keyboard ba-booms, mask a jaded, jazzy cool that fits both the character’s wise foolery and the production’s evocation of a fairy-tale world that’s wilting even as it’s blooming. Without hogging the moonlight, the ruffle-shirted, rug-sporting LeBow turns Twelfth Night, all by its lonesome, into a Shakespeare Feste-val.