A gritty, rock-inflected comedy using the nocturnal peculiarities of Mumbai slum life as a fertile (if at times fetid) palette, British-raised Karan Kandhari’s “Sister Midnight,” about a restless young housewife’s urban malaise, easily holds your attention for long stretches when seemingly little happens, but everything feels charged.

Don’t mistake this stylish feature debut for a misery wallow, however, or some poetic character study. It’s tantalizingly oddball and indelicate: a combined daymare and night odyssey that scratches until a feral hidden strength is revealed in the misfit main character, captivatingly played by Indian star Radhika Apte.

Though the movie ultimately can’t square its episodic unpredictability with the bubbling feminist-outlaw energy at its core — not to mention the comic-book twist that shakes it all up halfway through — that’s less a bug than a feature. Like a movie DJ, Kandhari is flexing a pulpy mood of big-city dislocation, building a trippy, jarring and blackly funny experience out of a city’s stray colors, sounds and personalities.

Arriving at their one-room hovel in the dead of night, arranged-marriage newlyweds and rural transplants Uma (Apte) and Gopal (Ashok Pathak) look more like thrown-together prison cellmates adjusting to a warden’s rules than a romantic couple embracing a future together. We glean that this was a match of undesirables: the timid, sexless guy no girl wanted and the girl too outspoken to be paired.

But here they are, having to make do. Gopal at least has a job to go to, from which he often comes home hammered after drinks with colleagues. Uma, left behind in the solitude of a shack that only allows one shaft of window light, is quick to profanely protest the joyless, intimacy-challenged rut they’ve entered. Alternating between angry and exhausted, she bristles at acclimating to the domesticity that her prickly neighbor wives treat like a club handshake.

Before long, Uma’s taste for cigarettes under the moonlight turns into regular solo walks at all hours. An impulsive journey to a coastal part of town hours away leads to her taking a cleaning job in an office building (and a friendship with a glumly simpatico elevator operator). Suddenly, she’s brandishing a mop and pail everywhere like a rootless knight without a quest or a horse. Then there’s a cryptic street encounter with a goat and things get even weirder. But also, somehow, more validating.

Kandhari, with his hypnotic Wes Anderson-by-way-of-David Lynch widescreen framing and deliberate tracking shots, seems more concerned with capturing something liminal in Uma’s alternative existence, as if the city were just weird and oppressive enough to tease out any transformation that was already lying dormant. (By the time the movie introduces stop-motion creatures roaming the streets, you’ve been primed to think, “Sure, why not?”)

A mischievously off-the-wall exercise like “Sister Midnight” (which eventually embraces some gnarlier elements) needs a certain steam to keep up its deadpan wildness. Kandhari is blessed in that regard with an active visual curiosity about his cracked fable’s punk potential, helped by Sverre Sørdal’s humid cinematography and a game lead in Apte, whose middle-finger energy is sometimes hilariously offset by a wonderful silent-film-star haplessness.

One wishes it all held together a little more, instead of laying seeds that tend to sprout vibes and distractions instead of an illuminating cohesiveness. Kandhari will too often keep Uma in cartoon rebel-goddess mode, needle-dropping another classic rock cut as if daring us to accept Motorhead or Buddy Holly as the only viable soundtrack for what’s going on. But those elements are a kick, too.

Of course, the title “Sister Midnight” is an Iggy Pop staple. “What can I do about my dreams?” it growls, an apt lyric for the singularly inventive and unmanageable fever of a movie that shares its name.