James (Sean Silvia - center) is bossed around by his mean aunts (L to R - Phillip Reid and Joe Brack) in James and the Giant Peach at Imagination Stage. (Margot Schulman)

Brave, ingenious James Henry Trotter — of “James and the Giant Peach” fame — is larking it up with Mick Jagger, Diana Rigg and the members of Monty Python’s Flying Circus.

Okay, that is not literally true. But in Imagination Stage’s enchanting production of “James and the Giant Peach,” sly echoes of 1960s pop culture reverberate through the strains of Roald Dahl’s 1961 story. The talking Grasshopper that James meets, inside the eponymous pitted fruit, swaggers around with an electric guitar in his grip, like a certain Rolling Stones singer. The lugubrious Earthworm sports a Nehru jacket. And when James’s parents travel to London, where they have the bad luck to be eaten by a rhinoceros, the city’s buildings plop down out of the sky like objects in the surreal animations created by Monty Python’s Terry Gilliam.

The tongue-in-cheek allusions give director Janet Stanford’s production an exhilarating polyphonic quality. At the same time, the show stays true to Dahl’s yarn, which tells how James escapes a miserable life with his cruel guardian aunts and travels across the Atlantic on the peach, in the company of the Grasshopper and other insects. (Imagination Stage is presenting “James and the Giant Peach” in repertory with “The Magic Finger,” a world premiere adaptation of a lesser-known children’s book by Dahl. David Wood adapted both shows.)

In Stanford’s version, James’s adventure is being turned into a movie, complete with breathless action sequences and 1960s-style pop songs. (Tim Guillot composed the music, which is original to this production; the lyrics are from Dahl’s book.) Milagros Ponce de Leon’s colorful scenery, anchored by a gnarled peach tree and an enormous peach pit, sometimes seems to be a film set. That’s especially the case when a production assistant (Megan Graves) wanders around with a clapper board; or when an appearance by James (a winning Sean Silvia at the reviewed performance; Ian Berlin sometimes plays the role) is underscored by a musical motif that recalls James Bond movies. (As Stanford has noted when discussing the inspirations for this production, Dahl wrote the screenplay for the 1967 Bond movie “You Only Live Twice.”)

But the movie-set conceit never overpowers the fantastical narrative, which kicks into high gear early on, with the appearance of Aunt Sponge (Phillip Reid, in a baby-doll dress and go-go boots) and Aunt Spiker (Joe Brack in comparably mod attire). Screeching at James and simpering or raging at each other, the aunts are delightfully grotesque comic villains, whose skullduggery heightens the euphoric excitement of James’s escape on the peach.

James has a plan to save the day in James and the Giant Peach at Imagination Stage. L to R: Eric Messner as Centipede, Lauren Du Pree as Miss Spider, Ian Berlin as James, Matthew Schleigh as Grasshopper, Leigh Jameson as Ladybug, and Phillip Reid as Earthworm. (Margot Schulman)

In the company of Matthew Schleigh’s moves-like-Jagger Grasshopper, Lauren Dupree slinks around engagingly as Miss Spider, looking in her leather outfit like Diana Rigg’s character in “The Avengers.” (Kendra Rai designed the pitch-perfect costumes.) Leigh Jameson makes an endearingly motherly Ladybird; Reid aces the Eeyorelike mopeyness of the Earthworm; and Eric Messner, draped in tiny boots, is enjoyably bossy as a Centipede who sounds like Michael Caine.

Stephen Guidry and David Stern’s effective and humorous video design helps evoke the supersizing of the peach, the menace of peach-chomping sharks, and the fruit’s arrival in New York City. Puppet designer Matthew McGee assists with the wondrous plot twists. (James’s fleeting underwater encounter with an octopus is a particularly nice James Bondesque touch.)

All in all, this is one of those productions where there’s almost too much to notice and relish at any given moment. Children at a recent matinee appeared spellbound. (Parents and other chaperones who want to explain the 1960s references at intermission will find a handy cheat sheet in the playbill.)

Older theatergoers who recognize the exuberant allusions immediately will find that they underscore, in a new way, the marvelous strangeness of Dahl’s tale.

Wren is a freelance writer.

James and the Giant Peach

adapted by David Wood from Roald Dahl’s book. Directed by Janet Stanford; music director, Deborah Jacobson; lighting design, Cory Ryan Frank; assistant lighting designer, Jedidiah Roe; sound design, Christopher Baine. About 90 minutes. Recommended as best for ages 4-10. Through May 26 at Imagination Stage, 4908 Auburn Ave., Bethesda. Call 301-280-1660 or visit www.imaginationstage.org.