Alejandro moves through New York with tiny steps, as if he’s on tiptoe, and wears a perpetual deer-in-the-headlights expression. He’s a stranger in a strange land, with the emphasis on strange: Everyone he meets is outlandishly eccentric to the point where you wonder if Alejandro has accidentally wandered into a cartoon.

Needing a sponsor to extend his visa so he can stay in the country to pursue his dreams, the aspiring toy maker finds himself in the orbit of Elizabeth, an ex-art critic with an explosion of red hair for whom screaming is a natural way of speaking. Played with manic abandon by Tilda Swinton (“The Killer”), Elizabeth is trying to organize a gallery show for her late boyfriend’s egg paintings, and Alejandro thinks he can help.

“Problemista” is one of those movies where every single character is ultra quirky and over-the-top, which can be exasperating. But there is something affectionate about writer-director-star Julio Torres’ approach, and it helps to think of his first feature film as one of his damaged toy ideas that needs a home.

Torres — a staff writer for “Saturday Night Live” from 2016 to 2021, co-creator, writer and executive producer of the HBO series “Los Espookys” and memorable as the caustic barista in “Together Together” (2021) — is known for his surrealist approach to comedy. But “Problemista” isn’t so much surreal as it is bizarre, like an “After Hours” for nerds (indeed, it has the vibe of a 1980s or ’90s New York indie).

Alejandro, who like Torres is from El Salvador, dreams of working for Hasbro, but he believes children should be preparing for the disappointments and awkwardness of life. His toys reflect that — a Slinky that can’t make it down the stairs, a jack-in-the-box that apologizes (“I’m sorry I was trapped in here and scaring you was the only way out”).

He takes odd jobs and finds himself working in a cryonics institute. One of the containers is filled with Bobby (RZA of the hip-hop group Wu-Tang Clan), Elizabeth’s boyfriend, who had himself frozen after he was diagnosed with terminal cancer. Alejandro is fired after accidentally unplugging the container (he plugged it right back in), but Elizabeth, raising hell with the institute over a price increase, takes him in.

Torres’ story isn’t great — “Problemista” feels like a series of sketches — but his ideas are interesting, sometimes even inspired. He also provides wonderful small roles for his cast, including Greta Lee (“Past Lives”) as Dalia, an artist with a grudge against Elizabeth, and Isabella Rossellini as the narrator.

The movie, though, is powered by the centrifugal force of Swinton’s performance as a manic-depressive whose bullying masks a deep loneliness. She finds the sweetness in what otherwise would be an unlikable character.

Reach G. Allen Johnson: ajohnson@sfchronicle.com