The story is admittedly odd, but the musical I Sent a Letter to My Love (lyrics and music by Melissa Manchester and Jeffrey Sweet) now running at the Katharine Cornell Theatre, has been stylishly packaged by Island Theatre Workshop. The storyline was adapted from a novel of the same name by Bernice Rubens, so perhaps the oddness may be laid at the feet of the author.

Set in the early 1950s in a small town, a sister cares for a wheelchair-bound brother stricken by polio at the age of eight. They live in loving yet lonely camaraderie on a lake. A nice woman named Gwen (Treather Gassman) moves into the guest cottage, newly liberated from a life of caring for a sick mother.

And of course everyone sings about everything, in that dissonant, expository style made popular by Steven Sondheim when a conversation about apples is something to sing about before it slips back into the chatter.

In a gesture that predates online dating by many decades, the sister, Amy (Melanie Sroka-Chaunce) sends an ad to the personals section of the local newspaper. The only response is, unbeknownst to him, from her brother, Stan (Aaron Duclos). The correspondence continues apace, with Stan mounting a growing passion, and Amy indulging in a guilty fantasy, not of romance with her brother exactly, but with the thermal fission of words themselves.

In addition, Amy has a fantasy lover, reincarnated from an actual lover from at least 20 years before, Jimmy (Crawford Scott), a classic sexy lounge lizard singer in a band, who passed through town and showered the young girl with affection, fun and lots of dancing — before he passed out of town forever.

A final figure enters the mix, Miss Morgan (Martha Hudson), an actress from a small community theatre who Amy hires to impersonate the passionate woman who has hooked her brother in Amy’s letters. And not to be overlooked is the lovely, shy Gwen, a flesh-and-blood woman who happens to be living on the property and, unconsciously or otherwise, is available for love.

The story posits a theme that, while composed in both the French and American novels in the 1970s, is well set in the 1950s: A person without a mate is doomed to be tragically lonesome until said mate is found.

Nonetheless we can fall into the cozy kitsch of this 1950s lakeside idyll where Gwen and Amy’s decision to wear pants is considered radical (and exciting when Gwen falls and splits hers up the back seam, to Stan’s great joy.)

The set design and construction by Brad Austin is picture perfect, a living-dining room of pale green walls, white wainscoting and daguerrotypes of Edwardian women, much like some of our great-aunts and grandmothers used to display. Vintage costumes have been lovingly curated by cast and crew.

Longtime ITW singer, director and administrator Kevin Ryan directs with polish and a seamless transition between song and words. Pianist Lisa Weiss is also a Todd Distinguished Professor at Goucher College in Baltimore, Md. Cellist Jan Hyer of Oak Bluffs plays in three chamber music piano trios.

Ms. Sroka-Chaunce is beautiful, poignant and endearing as the self-sacrificing Amy. Mr. Duclos, even confined to a wheelchair, has irrepressible charm, humor, and sex appeal — you can spend the entire play watching his changing facial expressions. Ms. Gassman makes the best of her role as superannuated love interest, and Mr. Scott and Ms. Hudson bring verve to their cameo parts.

There is no memorable melody to hum out loud as you descend the stairs of the grand old Cornell theatre, but there is plenty of discussion to be had with your companions before you part ways or run to get a late bite to eat (for Vineyard Haven anyway) down on Main street.

I Sent A Letter To My Love runs June 29, June 30, and July 1, 5, 6 and 7 at the Katharine Cornell Theatre in Vineyard Haven. All performances begin at 8 p.m. Tickets are $20 online at itwmv.org.