Viktor Gyllenberg, sitting center, in A Pigeon Sat on a Branch Reflecting on Existence (Magnolia Pictures)

“Hahahaha!” That’s the sound of a loathsome toy called “bag in laughs,” a periodic sinister backdrop to one of the most eccentric, highly stylized films you may ever see. If it’s not the oddest on your list, chances are at least it will end up in your top 10.

A Pigeon Sat on a Branch Reflecting on Existence is a hard film for which to prepare viewers. It is highly refined yet cussedly visionary and disinclined to compromise. Without giving away too much, here are some unyielding pillars which elevate Pigeon to a rarefied realm of its own.

Intriguing immobility: nearly every scene opens on a still or nearly still frame with unmoving human figures. Some stare into space like the lonely statues of George Segal. Others seem to sway slightly, recalling the standup cadaver in Blue Velvet but without the blood. Silent, motionless scenes draw in the eye before kicking into motion. During the entire film, the camera moves precisely once.

Painterly references: director Roy Andersson borrows washed-out, lonely tableaux from Edward Hopper. Diagonally framed scenes in deep, sharp focus, often with background figures on the left, evoke a digital Brueghel the elder or Andrea Mantegna, and trompe l’oeil teases perception. At the edges of this cultivated esthetic, more lowbrow influences lurk—the creepy cartoons of Gahan Wilson, perhaps. Light is flat, and the palette a mélange of white, green, cream, and a Scandinavian gray.

Elaborate artifice: all but a handful of scenes take place on sets. A bogus tavern hosts several different indoor scenes, but artificial streets and beaches dwell in grim yet lucid crepuscular glow. Gazing on them is like living in a dream where you see something that looks like a familiar object or setting, but which is essentially different from reality in a way you don’t understand.

Absurd and baffling situations: two cheerless and inept salesmen shuffle through town selling unappealing toys such as the “Uncle One-Tooth” mask. They sulk in their rooms or dodge creditors when they can’t make a sale (and they never do). Their encounters, full of failure, pathos, and dashed hopes, form a melancholy recurring motif—you can’t really call it a story line.

Other setups bring randomness to the edge of a very contained, specific madness. The film opens with three macabre rendezvous with death, one harshly funny. King Charles XII and his troops commander a modern pub on their way to the 17th century battle of Poltava against Peter the Great. A stout dance mistress puts the move on a wary student in an impressively choreographed number, delivered, like most of the film, in one cut. Rich partygoers look on at a horrific scene that denounces imperialism and technology in the drollest way ever. In this movie, expect to be startled.

A sense of timelessness: computers and cell phones coexist with retro gadgets and a carless, eerie quiet that’s anything but plugged-in. Sequences have beginnings, but most have no real ends. Some characters age. Others don’t. Again, the best way to describe the feeling of watching the movie is that it’s like being in a dream.

The sights and situations Andersson creates are fabulously unpredictable and singular. For such a virtuoso, he does not cut loose much at an emotional level. The whole film hatches in a deadpan space and never flies out of that nest. This presents limits for actors, who can’t show off their stuff much and mainly shamble and stare into nothingness. At their best, Andersson’s bizarre situations with their rejected, hopeful characters achieve a dark depth you might expect from Samuel Beckett. At its least inspired, this black comedy may bring sad clowns from the Cirque du Soleil to mind.

Reservations aside, Andersson has created something that casts powerful and perverse enchantments. It will linger with you—heartbreaking and delightfully weird.