First let’s get a few questions out of the way regarding “The Slug Bearers of Kayrol Island: Or, The Friends of Dr. Rushower.”

No, the slugs being borne aren’t slimy gastropods, but rather tiny ingots of lead. No, it’s not entirely clear where Kayrol Island is, but it’s somewhere in the vicinity of Borneo and it’s mildly sinister. And no, the cracked musical collaboration of the indie-rocker Mark Mulcahy and the retro-visionary cartoonist Ben Katchor isn’t nearly as precious or twee as that galumphing title would have you believe.

Their oddball parable of Western naïveté in the face of globalization has its ungainly moments, to be sure, albeit nearly always tempered by the dazzling use of Mr. Katchor’s fancifully old-timey illustrations on all sides of the stage. Director Bob McGrath and the wonderfully skilled projection designers Jim Findlay and Jeff Sugg have turned the Vineyard Theatre stage into a three-dimensional graphic novel, with Mr. Katchor’s perspectival contortions and multi-panel wonders augmented and sometimes mirrored by Mr. McGrath’s wily staging. They have collaborated on devising an intoxicatingly cluttered world where the margins have taken over the center.

After a cryptic anonymous phone call between the unfulfilled Gingin (Jody Flader) and an alluring stranger named Samson (Matt Pearson), the “plot” begins in earnest with a sung lecture from Gingin’s stepfather, Dr. Rushower (Peter Friedman), on the use of those aforementioned slugs. Basically, they make the ever-shrinking mechanics of modern technology seem more substantial by weighing down the appliance in question: “And thus … blenders can resist the pushing of their buttons.”

One would think that such lectures might encourage the appealing Gingin to get out more, but Dr. Rushower has been reduced to luring one suitor after the next to their penthouse apartment, often by dropping food on them. His latest candidate is Immanuel Lubang (Bobby Steggert), a defiant young Luddite who derives much of his joy from public readings of the instruction manuals to such long-discarded products as the Glama-House Never Burn Toaster.

Gingin’s newfound compulsion for the migrant workers who are forced to carry all of those lead slugs dovetails with Immanuel’s passion for old-school appliance design and Dr. Rushower’s matchmaking goals — until a philanthropic voyage to the island in question results in disillusionment, cultural miscommunication, enormous consumption of the aphrodisiacal Kayrol Cola, and a newfound appreciation for “labor divorced from purpose.” As if this weren’t a sufficiently murky story to tell, Messrs. Katchor and Mulcahy have decided to do it entirely through song. David Yazbeck (“Dirty Rotten Scoundrels,” “The Full Monty”) might be the closest corollary to Mr. Mulcahy among current theater composers, but the more apt comparisons would be to pop songwriters Ben Folds and Tom Waits, and especially Andy Partridge, the principal force behind the nuts-and-bolts psychedelica of XTC. Many of Mr. Mulcahy’s songs morph into tantalizing demi-melodies that fall into a surprisingly comfortable middle ground between recitative and full-throated song — a sort of sonically compelling, harmonically curious vamp. Mr. Katchor’s lyrics are similarly unconventional. Though a welcome and possibly even essential development in today’s musical theater, the influx of pop-savvy songwriters has resulted in a dip in standards when it comes to rhymes. This has nothing to do with the assiduously crafted infelicities of Ira Gershwin and Cole Porter; Mr. Katchor frequently dispenses with verse altogether, but when he does attempt it, the results will hardly put at ease those purists who grumble about the imprecise rhymes in “Spring Awakening.”

As far as the six men and one woman entrusted with singing these lyrics, Mr. Friedman gives his electrolycist/procurer/philanthropist a hearty blend of gravitas and deadpan wit, while Mr. Steggert and Ms. Flader fare well with their strangely earnest protagonists. If a few of the supporting roles succumb to overly broad, audience-nudging conceptions — Will Swenson as a Lothario of a psychiatrist, Stephen Lee Anderson as a villainous factory owner — perhaps Mr. Katchor’s off-kilter scenarios wear better with added familiarity. (While he has contributed weekly cartoons for the Forward and several alternative newspapers for more than 20 years, he remains far better known for the published collections of these extended stories.)

The slug bearers are about as captivated by the inner workings of the Dunscap Electric Coffee Maker as you’d imagine them to be. But with Mr. Katchor’s beguiling illustrations guiding the way, their architectural solidity accentuated by the occasional dashed-off line or disproportionate detail, a similar frisson of neo-retrotimelessness washes over the audience as well. The notion of a tribe of New Yorkers prostrating themselves to the antiquarian charms of old instruction manuals suddenly doesn’t seem quite so ludicrous when these manuals are described as “that form of prose poetry known as ‘consumer fiction.'” Or rather, it sounds even more ludicrous — and intriguing at the same time.

Until March 2 (108 E. 15th St., between Park Avenue South and Irving Place, 212-353-0303).