There’s a cozy ease that permeates “All In,” in which a rotating cast of celebs narrates, with both flourish and offhandedness, the humorous and offbeat essays of The New Yorker writer Simon Rich.

It’s the kind of comic comfort that easily fits into the holiday period but also into a Broadway season that is especially welcoming to laughter.

But “All In” brings a different kind of comedy to the stage, a gentler kind of wit, packaged at a modest length and in a minimalist form, though elegantly staged by Alex Timbers and designed by a theatrical A-team: David Korins (sets), Jake DeGroot (lights), Peter Hylenski (sound), and Jennifer Moeller (costumes), among them. Lucy Mackinnon provides the video design featuring Emily Flake’s whimsical drawings.

Think of it all as a hipster “Love Letters” in a loft setting: quirky, absurdist, sometimes rude but never crude (well, maybe the humping dog bit). Or perhaps Garrison Keiller on psychedelics.

The eight stories include such fanciful characters and perspectives as a hard-of-hearing genie, parental pirates, dogs on the make and even the Elephant Man, ostensibly linked by characters finding unexpected connections. But more than that it’s about commitment, and being “all in” in any number of amusing and awkward ways, with just a wisp of sentiment. Some fit nicely into this theme while a few feel a bit shoehorned in.

The show’s limited Broadway run starts its first weeks with a solid quartet of high-profile narrators: Rich’s comedy bro John Mulaney leads off the show that also includes Richard Kind, Fred Armisen and Renée Elise Goldsberry. They are seated (but not always) in comfy armchairs and are reading (but not always) off of oversized books which contain the humorous essays by Rich, who has also written for “Saturday Night Live,” “The Simpsons” and Pixar films. (Of note to theater wags: He is also the son of former New York Times critic Frank Rich.)

Nestled between the stories, as well as underscoring them, are the love songs and music by Stephin Merritt of Magnetic Fields. They are sung by indie folk-rockers Abigail and Shaun Bengson, whose “Hundred Days” musical memoir was an Off Broadway treat in 2017. Abigail’s sterling voice especially resonates with Merritt’s rich melodies and wry lyrics, and kicks off the show with the appropriately named “Absolute Cuckoo.”

But the loopiness starts off a bit awkwardly with Mulaney narrating in his trademark smoothie style, sans script and standing, a yarn about a genie, a bartender and his 12-inch pianist, a kind of shaggy dog tale that glides into a too-soft landing. Mulaney finds his groove in subsequent, sharper stories, with his best turn delivering with Sam Spade snap the tale of the toddler detective on the case of a missing plush toy owned by Baby Zoe from the white bassinet down the hall (Goldsberry).

Kind demonstrates his emphatic comic range both vocally and physically — even getting laughs from variations of chair slouching — as a jealous doctor whose wife bonds with the Elephant Man.

Armisen voices a number of droll characters and is hilariously — and fittingly — deadpan as the figure of Death who becomes seduced by show biz via a clever agent (Kind).

Despite the wild characters and imaginative leaps, the humor is laidback, pleasant, and effortless, more likely to elicit warm smiles than thigh-slappers. It’s at its most reflective in the final piece.

Set in 2074, the story has Rich’s imagined great-granddaughter interviewing him for a school paper where they now live on “New Earth” (climate change, you know). When she asks him about his favorite memory, he recounts, instead of stories from World War IV, the tale of his courtship and long marriage with his wife, involving dating rituals, sex robots and “Arrested Development.” Goldsberry is both funny, guileless, and dear, and ends the show with a kind of light wave, a gentle gesture for what turns out to be a very good night.