“Randy” of The Residents performs at 6th and I Synagogue in Washington, D.C. The group, which keeps their identities secret, has released over sixty albums during the course of their career, including last year’s “Coochie Brake.” (Kyle Gustafson/For The Washington Post)

The most conventional thing about the Residents’ 40th-anniversary tour is that it actually marks a 40th anniversary: In late 1972, the mysterious California art-rock cabal issued its first single, “Santa Dog.” In honor of that tune, the musicians performed Sunday night in front of large inflated figures of Santa and a snowman, both holding candy canes. Visually, the D.C. stop benefited from a special irony: Its venue was the Sixth & I Historic Synagogue, so the big blow-up Santa stood under a bigger stained-glass window featuring a Star of David and a menorah.

The Residents labor anonymously, and while much has been reported about them, nothing has been officially confirmed. Currently, the performing version of the troupe has three members, identified as Randy, Chuck and Bob. Frontman Randy and keyboardist Chuck may actually be founding members Homer Flynn and Hardy Fox. Then again, maybe not.

If Flynn and Fox remain active Residents, nearly everything else has changed since 1972. The group originally made collaged music, back when “cut and paste” was not a computer term. Time and technology overtook their style, which now combines monster-movie scores, fractured prog, ’80s-style industrial and demented art-rock. On stage, this jumble of genres was produced primarily with Chuck’s laptop and Bob’s electric guitar. The digital era has made sonic bricolage much simpler.

The Residents may have been working together since 1969, but didn’t tour until 1982-83. (Another anniversary!) That jaunt was a financial debacle, but the group subsequently became a medium-sized concert draw. It played local venues as ample as Lisner Auditorium, using complicated staging and costumes. The latter included head-enveloping eyeball masks that became the group’s visual trademark. Those disguises were invoked but not employed in Sunday’s nowhere-near-sold-out show, which clearly had a limited props budget. Randy relied heavily, for example, on a red swivel chair.

The musicians’ secrecy requires some sort of disguise, of course. Chuck and Bob wore black hoods with goggles and dreadlocks, so they resembled Rastafarian ant-people. Chuck partially hid his face with prosthetic features, adding a bald cap framed by mad-professor hair. For a man in the conceptual-art protection program, though, Randy was surprisingly chatty about the band’s history and his personal life. Much of his patter was dubious, but some stories — such as one about the untimely death of collaborator Phil “Snakefinger” Lithman at 38 — were true.

While Randy’s recollections covered the Residents’ entire career, the set list emphasized more recent material. The encores, however, evoked the group’s earlier days and aesthetic. As an eyeball-topped vinyl Christmas tree inflated, “Santa Dog” mutated into a Hendrix-style “Happy Birthday,” and then “Mahogany Wood” yielded to an orchestral “Auld Lang Syne.” Nostalgia has rarely been weirder.

Jenkins is a freelance writer.