David Gamble, Elliott Bales, KyoSin Kang, Karina Hilleard, Carolyn Kashner, Adi Stein, Ben Chang and Luke Ceislewicz in the Theater Alliance production of “The Wonderful World of Dissocia.” (C. Stanley Photography)

These individuals are so outlandish, they make the Mad Hatter look like Miss Manners and the March Hare look like the Easter bunny. There’s the watch-repair specialist who drinks urine; the bumbling, ritual-addicted bureaucrat known as the Oathtaker; and the talking goat who hungers for blame (he’s a scapegoat, you see) and who turns out to have a shocking propensity for violence.

These and other zany characters give a bracingly weird luster to “The Wonderful World of Dissocia,” the intensely funny and unsettling play that Theater Alliance has staged at the Anacostia Playhouse. Written by contemporary Scottish playwright Anthony Neilson — and ably directed here by Colin Hovde and Nathaniel Mendez — “Dissocia” piles quirk upon quirk, and disturbing detail upon disturbing detail, until the fever-dream storyline becomes just a touch exasperating. And then, with a sudden plot twist it would be a shame to reveal, the weirdness pays off and the play gains a new layer of emotion and meaning.

Giving visual expression to Neilson’s 21st-century, R-rated Wonderland, set designer Collin Ranney inks the walls of the cavernous Playhouse space with blotches of blue, green and pink that evoke a kindergartner’s painting. (John Burkland contributes the suitably dreamlike lighting.) What look like brown pebbles cover the floor. When we first encounter this decidedly uncozy landscape, it appears to stand in for the apartment inhabited by Lisa (Karina Hilleard), the play’s Alice figure, first seen seated on the pebbles, surrounded by shelves and trunks.

Lisa has been out of sorts lately, so when the watch-repair specialist (Elliott Bales) diagnoses her problem as a lost hour — the 60 minutes went AWOL during a transatlantic flight, apparently — she agrees to seek her missing stretch of time in the land of Dissocia. During the course of her quest, she meets, among other oddball figures, the Oathtaker (Dave Gamble), the friendly but neurotic Insecurity Guards (Carlos Saldana and Luke Cieslewicz) and Jane (Lisa Hodsoll), whose job it is to be the victim of every crime in the area.

Jane moonlights as a bomber pilot in Dissocia’s ongoing war with a sinister figure known as the Black Dog King. (The sound design by Matthew M. Nielson and Christopher Baine helps conjure up the war, among other phenomena.) As danger becomes more apparent, wordplay runs riot — another parallel with Lewis Carroll — and the lunatic logic of Dissocia stymies Lisa’s search for her hour, you begin to wonder whether the story is all that it seems. (Theater Alliance staged Neilson’s “The Night Before Christmas” in 2012.)

Act II could use a tighter rhythm, but directors Hovde and Mendez have done a fine job calibrating the look and pace of Act I, including several multi-character scenes that come across as both truthful and hallucinatory. And the performances hit the right notes of kookiness and menace. Dressed youthfully in a ­floral-pattern dress and tights, her hair in a braid, Hilleard’s Lisa is an appealing protagonist, by turns persuasively plucky, infuriated and anxious. Hodsoll’s Jane is striking and funny, while Adi Stein, as the top-hat-sporting Goat, adroitly fuses goofiness and depravity. (Ranney designed the steampunk-flavored costumes.)

“Dissocia” is not a play for timid theatergoers. Its lost-in-the-fun-house storytelling can be relentless, and one of the violent crimes to which Jane submits, while not graphically depicted, registers in a deliberate and horrifying way.

But audiences who appreciate distinctive and provocative visions will find this production a memorable experience. “A stray hour is a source of tremendous energy,” the watch-repair specialist remarks early in “Dissocia.” The same could be said for a 2 1 / 2 hour stretch that’s filled with an intriguing, challenging play.

Wren is a freelance writer.

“The Wonderful World of Dissocia”

by Anthony Neilson. Directed by Colin Hovde and Nathaniel Mendez; original music, Matthew M. Nielson. With Carolyn Kashner, Ben Chang and KyoSin Kang. About two and a half hours. Tickets: $20-35. Through
June 28 at the Anacostia Playhouse,
2020 Shannon Pl. SE. Visit www.theateralliance.com
or call 202-241-2539.