“Wiener-Dog” isn’t so much a cohesive movie as a collection of four disjointed shorts. Divided into two groups of two by a jaunty musical intermission, the segments are connected by a worried-looking brown dachshund that shows up in every story. Tone is the other constant: a sardonic sense of melancholy you’d find in any movie by writer-director Todd Solondz (“Happiness”).

“Wiener-Dog” opens with a man offloading the title character at an animal shelter. Finding itself inside a small crate alongside the pens of other castaways, the dog paces aimlessly. Around and around it goes, and the camera doesn’t budge.

That’s another hallmark of Solondz: forcing the viewer to linger well beyond what’s expected or what’s even comfortable, holding focus, for example, on a young boy staring at the sky while lying in his backyard. The fact that the kid doesn’t blink gives the disconcerting impression that he may not, in fact, be breathing.

Not to worry: His name is Remi (Keaton Nigel Cooke) and he becomes the new owner of Wiener-Dog, a surprise gift from his father (Tracy Letts). Remi is instantly smitten. His mother (Julie Delpy) is less enthused.

“Now who’s going to walk it?” she spits at her husband. She’s more patient with her son, even though he’s prone to interrogations, asking questions about everything from canine reproductive urges to faith.

“What does it feel like to be put to sleep?” he asks, after learning about dog euthanasia. “It feels good!” his mother says, cheerily. “Like forgetting everything.” Upon hearing that his family doesn’t believe in God, Remi wonders what they do believe in. “Truth, compassion, love,” his mother responds angelically, without even a hint of irony.

Another story revisits two characters from Solondz’s 1995 breakout feature “Welcome to the Dollhouse,” this time with different actors: Greta Gerwig as former grade-school nerd Dawn Wiener, and Kieran Culkin as the former bully Brandon. After running into each other at a convenience store, the two end up taking a impromptu road trip together, along with her dog, this time named Doody. (The name inspired by “Howdy Doody,” although most people think it’s something else.)

Then there’s the lonely screenwriting professor (Danny DeVito), who’s practically invisible. In the final installment, Ellen Burstyn plays a salty, ailing woman, who’s cruel to her freeloading granddaughter and only slightly kinder to her dog, Cancer.

This segment takes a turn for the surreal when several identical little girls show up to explain to the woman all the different people she might have become if she’d made different choices. But it’s still firmly rooted in the director’s particular brand of earthiness. The camera holds steady as Burstyn swills gulp after gulp of Kaopectate, straight from the bottle, until long after you’re sure the container must be empty.

Solondz is an acquired taste, but at least he’s consistent. The same way Wes Anderson serves up elaborate set pieces — not to mention elaborate sets — Solondz revels in rusty minivans and moth-eaten couches. His characters aren’t stylish, or even all that appealing. They’re just everyday people going about their lives.

You wouldn’t exactly call the movie a thrill, but it’s curiously engrossing all the same.