In out-there Estonian comedy “The Invisible Fight,” a clueless Russian border guard somehow escapes a surprise attack by three formidable Chinese action figures — gravity-defying kung fu warriors who swoop in out of nowhere, blasting Black Sabbath on their bright red boombox — so he does what anyone in his position would do: He resolves to become an Orthodox monk. Huh? “I guess God has other plans for you,” a less-fortunate comrade wheezes with his dying breath, setting up one of the oddest plots audiences are likely to find on the art-house circuit this year.

After attracting international attention with 2017 festival discovery “November” —a hyper-stylized, black-and-white folk horror novelty involving pagan stick monsters known as “kratts” — writer-director Rainer Sarnet swings to the color-saturated opposite extreme to make a genre-splicing martial arts satire. Set in the highly repressive, mid-’70s Soviet Union and shot like a vintage drive-in movie (complete with smash-zooms, optical titles and virtual wear and tear), “The Invisible Fight” treats kung fu as comedy, landing like a cross between “Shaolin Soccer” and “Gymkata,” but with better production values … and Orthodox monks.

It’s a wacky and frequently nonsensical mish-mosh of elements that don’t quite add up, and yet, the absurdist shock of seeing such incongruous ingredients forced together is typically enough to spark laughter. Consider the sight of a long-haired heavy metal fan in a black cassock hovering in mid-air as he faces off against an incredulous KGB officer.

Sarnet’s script centers on Rafael (wild-eyed Nicolas Cage lookalike Ursel Tilk) and his personal quest for spiritual enlightenment — except that in this case, Rafael’s reason for joining an Orthodox monastery isn’t remotely religious. In the movie’s profane parallel reality, Orthodox monks guard the secrets of “black metal kung fu,” which means Rafael’s only hope of learning the technique is to dedicate himself to the faith. That may be true of Shaw Brothers movies set in Shaolin temples, but it feels strange watching chanting Russian starets doing back-flips in church, much less trying to reconcile how a screw-up like Rafael fits into their relatively ascetic enclave.

“Everything cool is banned in the Soviet Union,” grouses Rafael, who grows his hair out and gets a job as a car mechanic after surviving the film’s kooky opening showdown. That fateful run-in with the three wuxia assassins impresses Rafael, but doesn’t immediately inspire him to learn self-defense. Instead, his big conversion comes later, after Rafael takes a fist to the face for dancing with a local tough guy’s comely fiancée. The woman, Rita (Ester Kuntu), is meant to embody a certain Russian ideal: a buxom lass with heavy lipstick and a permanent scowl. Rafael finds her irresistible, but unavailable — and so he commits himself to monastic life.

Sarnet isn’t always clear about what exactly seems to be going on inside the head of his doofus hero, which is ironic, considering that after a few weeks’ training, Rafael can literally read other people’s thoughts. Between this and other religious miracles, Rafael is seemingly destined to be a disciple. At least, that’s what giggling lead staret Nafanail (Indrek Sammul) seems to believe, much to the chagrin of his not-so-humble protege, Irinei (Kaarel Pogga), who tries to sabotage the newcomer’s progress. Cue one of the movie’s more amusing altercations: a food fight involving raw dumplings.

As the film’s title sorta-kinda suggests, “The Invisible Fight” finds Rafael torn between spiritual clarity (on one hand), his rebellious punk persona (on the other) and Rita’s more carnal charms (on still a third). That’s at least one hand too many as the movie juggles these seemingly contradictory ingredients. How to reconcile Rafael’s violent kung fu training with his search for inner peace, for example? And where are his hot-blooded romantic ambitions supposed to fit into the picture?

The monastery business begs to be taken seriously, and yet, the project’s kitschy color palette and slapstick acting style suggest a live-action Saturday morning cartoon, complete with silly sound effects (from exaggerated eye blinks to tweety-bird knockout noises). Whatever statement Sarnet’s trying to make about Rafael’s religious calling winds up smothered by surrealism. It’s all weird enough to amuse those looking for a gonzo good time, even if the eccentricity doesn’t add up to much.