Left to right, Richard Jenkins, Debra Winger and Evan Rachel Wood in “Kajillionaire.” Matt Kennedy/Focus Features

Fans of Miranda July know what they’re in for when they settle in to watch one of her movies. Since her 2005 feature debut “Me and You and Everyone We Know,” and her follow-up “The Future” in 2011, she has become the kind of writer-director whose work inevitably seems to be described as “quirky.”

Whereas that word may be accurate, it’s also unjustly reductive, distilling July’s unpredictable, self-conscious and acute sensibilities into a catchphrase that is suspiciously close to “kooky.” Anyone relegating the work of this thoughtful, rigorously disciplined artist to those patronizing margins does so at their peril.

The opening scene of “Kajillionaire” gets that point across as well as anything. Filming her protagonists from a distance, against the backdrop of a pastel-blue Los Angeles post office, July stages the sequence less like a movie scene than a dance, or piece of performance art: Robert (Richard Jenkins), Theresa (Debra Winger) and their young-adult daughter Old Dolio (Evan Rachel Wood) are clearly up to something, barking signals to each other with cryptic verbal shorthand until Old Dolio jumps over a wall and slithers into the building with startling dexterity.

The sequence suggests that the story about to unfold will be rife with stylized oddball flourishes for their own sake. But it turns out that everything and everyone has their reasons in “Kajillionaire,” in which July turns her exacting eye to the outer edges of the American political economy. Robert, Theresa and Old Dolio live like modern-day urban gleaners, scrounging and running petty cons to put a few dollars together for their subsistence living. While most of their fellow citizens yearn to amass the sudden super-wealth to which the title refers, Robert has adamantly refused to play along. “I prefer to just skim,” he says at one point.

So far, so quirky – kooky, even. But what appears to be a wry portrayal of eccentric off-the-gridders becomes something much weirder, deeper and more unsettling as “Kajillionaire’s” true subject matter emerges. The film is spiked with amusing touches, especially the off-kilter physical comedy at which July excels. (The family’s methods of avoiding their landlord are particularly funny; a recurring cascade of anarchic pink bubbles also provides a lighthearted visual motif.) When they meet an outgoing Angeleno named Melanie (Gina Rodriguez) on their peregrinations, the effect is twofold: The arrival of a stranger injects a welcome note of pseudo-normalcy to Robert and Theresa’s hermetic lifestyle, but it also throws that lifestyle into relief that points up its darkest contours.

Evan Rachel Wood in “Kajillionaire.” Matt Kennedy/Focus Features

That’s especially true when it comes to Old Dolio, whose name is explained partway through the film (let’s just say it’s on-brand for Robert and Theresa’s utilitarian approach to life). Played by Wood with stony-faced dispassion behind a curtain of never-cut hair, this enigmatic young woman emerges as the unlikely pulse of “Kajillionaire,” as her idiosyncrasies reveal themselves to be closer to primal wounds. Everyone in the film is in top form, from Rodriguez’s bubbly obliviousness and Winger’s tight-lipped sincerity to Jenkins’s deadpan delivery of some of “Kajillionaire’s” funniest lines. But the story belongs to Old Dolio, and to Wood’s surpassingly delicate performance, which entails not just full physical commitment to a part that demands nothing less, but an emotional transformation as exhilarating as it is painstakingly incremental.

Funny, poignant and ultimately triumphant, “Kajillionaire” is a precarious balancing act, one that July pulls off with astute writing, careful staging and trust in her actors to strike precisely the right emotional tones, whether they be tender or breathtakingly tough. July’s dexterity is exemplified in one memorable scene, set in the home of one of their marks, when Robert, Theresa, Old Dolio and Melanie slip into their own pantomime of a happy family: The sequence flows from perverse humor to unexpected poignancy to Darwinian ruthlessness with startlingly organic ease. Quirky? Sure, but it’s so much more than that. It’s Miranda July, at her closely observed and compassionate best.