A scene from Happenstance Theater’s “Pantheon.” (Ryan Maxwell Photography)

Stationed at the entrance to Hades, the three-headed guard dog Cerberus has seen it all. Or maybe not: The monster has apparently never confronted a mortal singing “How Much Is That Doggie in the Window?” Warbled by that dashing crooner Orpheus, the ditty proves so soothing that Cerberus nods off. Orpheus sneaks by, into an underworld filled with imperiled love and shadowy, slapsticky torments.

The sequence epitomizes the intriguing tonal chiaroscuro in “Pantheon,” a rewarding, if not entirely flawless, riff on Greek mythology by the distinctive Happenstance Theater. The troupe’s sui generis productions — skits, movement-rich vignettes and musical interludes, linked by retro motifs — are typically feats of comic whimsy, sometimes flecked with wistful lyricism. In “Pantheon,” an unusual somberness weaves through the mix, hinting at serious existential and topical concerns: loss, futility, environmental devastation. Also at issue: Is it a good idea to sleep on a beanbag chair?

The darker currents in “Pantheon” gain strength from the Depression- and World War II-era imagery the troupe has laid over the classical source material — an attempt to create a “cultural/historical bridge” between ancient and modern times, as a program note explains. Deftly and amusingly channeled by Happenstance’s Mark Jaster, Sabrina Mandell, Gwen Grastorf, Sarah Olmsted Thomas and Alex Vernon, the show’s mythological protagonists recall the likes of WPA posters and 1940s pop culture.

Seeking to rescue his wife, Eurydice, from Hades, Orpheus (Grastorf) is decked out like a big band leader. The bickering goddesses Hera, Athena and Aphrodite (Mandell, Grastorf, Thomas) sing an Andrews Sisters-style number. And the sun god Helios’s troublesome offspring, Phaethon (Vernon), sits on a construction girder with fellow workers, evoking the famous 1932 photo “Lunch Atop a Skyscraper.”

Phaethon’s catastrophic attempt to cash in on his relationship with Helios (Thomas) triggers some of the show’s more sobering reverberations (think climate change). Also tinged with ominousness — but with farcical undertones — are the Hadean torments, niftily conjured through shadow puppetry. The silhouettes harmonize with the show’s overall spare aesthetic, whereby mime substitutes for special effects and the scenery consists of ladders and planks. (Vernon designed the puppets and Mandell, the costumes.)

Over to one side of the stage, guest artist Craig Jaster (Mark’s brother) sings and plays multiple instruments, interpreting period tunes (e.g., Cole Porter) and also jaunty period-esque music of his own composition.

The show’s opening mime sequence could stand refinement, as it is occasionally unclear and doesn’t link the mythological and American-history themes in a wholly satisfying way. Later on, in a subplot about bees, the pacing flags.

But the many droll and stylish scenes make up for those deficiencies. In the show’s high point, a hilariously wary-looking Mark Jaster reads questions to the Oracle, portrayed by a blindfolded Mandell and Vernon. The two-bodied Oracle retains priceless gravitas as the questions prove wholly unworthy of divine expertise. (“O Oracle, do you play Fortnite?”) And, yes, the Oracle has an opinion about sleeping in that beanbag chair.

Pantheon Music composed and/or arranged by Craig Jaster; lighting, Kris Thompson. 75 minutes. Through July 1 at Joe’s Movement Emporium, 3309 Bunker Hill Rd., Mount Rainer, Md. $17-$23. happenstancetheater.com.