One would be sorely pressed to find a more unconventional musical theater ingénue than the title character in “Kimberly Akimbo.” In some ways, this heroine is a typical teenager, albeit of the precocious, nerdy variety who wears jump dresses over striped shirts, adorns her bedroom with string lights and posters, and crushes on a sweet, similarly nerdy guy in her high school class.

Kimberly also suffers from a rare genetic disorder, one that causes her to physically age at between four and five times the rate she should, so that on the brink of turning 16 years old — the average lifespan for a person with her condition — she has the body of a woman roughly in her 70s. As she sings to her peers in a moment of piqued despair, “Getting older is my affliction/Getting older is your cure.”

While this plight would hardly seem like fodder for musical comedy, “Akimbo” — adapted by David Lindsay-Abaire from his 2001 play, with music by Jeanine Tesori — turns out to be as exhilarating as it is heartbreaking. Under Jessica Stone’s exuberant, loving direction, a youthful cast led by 63-year-old Victoria Clark deliver what is at once a meditation on mortality and a thoroughly, giddily life-affirming experience. 

We meet Kimberly as she is waiting for her alcoholic father to pick her up from the local skating rink in Bergen County, New Jersey; the state will be the butt of numerous jokes, which Mr. Lindsay-Abaire somehow manages to make funnier even as they become more predictable. The playwright, who crafted the show’s lyrics as well as its book, also mines the humor in Kimberly’s fraught family life, which involves a pregnant mother recovering from carpal tunnel surgery and an aunt on the lam after the latest in a string of crimes and misdemeanors. 

At the same time, we’re shown how cruelly this teenager suffers for her relatives’ irresponsibility and insensitivity. Her parents, Buddy and Pattie, who married as high schoolers themselves after Pattie fell pregnant, make no secret of their enduring disappointment, and it is Kimberly who has to tend to them, rubbing her mother’s feet and procuring coffee so that her dad can drive home safely after hitting the bar again.

Rather than being thanked, Kimberly must listen as Pattie rubs her swollen belly and declares, “I want this one to be perfect,” or as Buddy, after seeing his daughter with makeup on, observes, “You look like Nana at her wake.”

Yet “Akimbo” has far too big a heart to demonize any of its characters. Pattie and Buddy and even, to some extent, Kimberly’s Aunt Debra — an amoral, scheming parasite brought to blazing life by a hilarious Bonnie Milligan — emerge as men and women with their own struggles. In a moving scene, Pattie, who in Alli Mauzey’s pert performance becomes a model of aggravation tempered by zaniness, segues from singing to her unborn child to addressing her disease-addled daughter with the same lyric: “Father Time, slow down the day/Don’t let the dark come/And steal it away.”

Ms. Tesori, whose previous credits include celebrated musicals such as “Fun Home” and “Caroline, or Change,” accommodates the show’s emotional range with melodies that alternately rouse, soothe, and haunt. A standout is “Good Kid,” a pining ballad sung by that sweet nerd who befriends Kimberly, Seth — played by the hugely endearing Justin Cooley, who collected a bevy of awards after this show premiered off-Broadway late last year.  

The anchor of “Akimbo” is, of course, Ms. Clark, whose ability to ooze girlish buoyancy while evincing the ravages of age and sickness is astonishing. Interacting with Mr. Cooley, and with other talented young performers who play members of the school’s delightfully goofy show choir, the veteran actress conveys how the frisky energy and awkwardness of youth threaten to overwhelm Kimberly at times. The extremes of joy and sadness that normally accompany adolescence are right there, only contained in a clearly withering frame. The impact can be devastating. 

Joy finally wins in “Kimberly Akimbo,” though, as it must. Life is short for everyone, and Kimberly’s ultimate insistence on savoring whatever sliver she’s given is nothing short of inspiring. It’s an example that trauma-obsessed Generation Z-ers would do well to heed, and one that should uplift all of us.