Radio storytelling took the stage on Friday and Saturday nights, when performance artist Dan Froot brought his acclaimed show Pang! to the Martha’s Vineyard Playhouse as part of the Yard’s offseason programming.

Mr. Froot and the members of his company came not only to perform their work about families living with food insecurity, but to do it with an informed understanding of the Island and its food needs. In the days running up to their show last week, the four performers volunteered at the Island Food Pantry and with Island Grown Initiative, where they helped glean fall vegetables from farm fields and make them into soup.

“That day we were short on volunteers, so it was awesome,” said food pantry executive director Kayte Morris, one of many Vineyard nonprofit executives and volunteers who turned out for Pang! on Friday.

The troupe also paid tribute to the original Islanders in a program note acknowledging that “the land on which we gather is the territory of the Wampanoag and Algonquin peoples. . . We thank them for their strength and resilience in protecting this land, and aspire to uphold our responsibilities according to their example.”

Pang! is both a stage play and a podcast series the New York Times has called “an experiment in the dynamic power of the podcast medium as it endeavors to answer the question, ‘What does hunger sound like in America?’”

Based on in-depth oral histories of families in Los Angeles, Cedar Rapids and Miami, the stage version of Pang! uses techniques from old-time radio to bring their stories to life. Mr. Froot, a professor in the University of California, Los Angeles Department of World Arts and Cultures/Dance, is the show’s narrator and sound-effects man as well as its producer, writer and director.

Pulling up music cues from a laptop, Mr. Froot created many of the sound effects manually and with such attention to detail that when he switched a bedside lamp on and off into the microphone, it was plugged in so that the bulb lighted up as well.

With only their voices, and the occasional paper coffee cup to add a phone-line effect, actors Natalie Camunas, Lorinda Hawkins Smith and Christopher Rivas compellingly took on the roles of six adults and a dozen children in three families who have limited access to food. At times, the actors spoke in unison. At others, they played both roles in a dialogue, as when an elderly Filipino-American homeowner talks with the “Filipino brother” who has befriended his large extended family in order to cheat them out of their home.

The fact that both characters were voiced by Mr. Rivas took nothing away from the audience’s growing dread as they watched the mortgage scam unfold, with Ms. Camunas and Ms. Hawkins Smith playing the homeowner’s daughter, her nine children and the scammer’s accomplice at the mortgage company.

This story, which became the first episode of the podcast, illustrates the limitation in calling Pang! a work about food insecurity—food barely rates a mention in the predatory tale.

“We’re not telling stories about food insecurity. We’re telling stories about people. People who happen to be living with food insecurity,” Mr. Froot wrote in his program notes for the playhouse show.

The other two families in Pang!, a Burundian refugee and his teenaged daughter in Iowa and an African-American family in Miami’s Overtown neighborhood, also have more than food on their minds. In a wickedly satirical play-within-a-play, Mr. Rivas plays an unctuous podcast host for a refugee charity, trying to elicit from his guests just the right response to turn on the donors’ money faucet. The last story brought the audience into a family touched by street violence and institutional racism in a long-segregated Miami neighborhood, where a little boy named Terrence imagines being a shark and learns that his best friend was killed by a stray bullet—one in a long list of children who have died by gun violence there. Reciting the young victims’ names one by one, the performers let pages of their scripts fall to the stage until it was littered with white sheets of paper.

About a half-dozen audience members watched the performance from an onstage table set with water and fruit, where Mr. Froot invited them to start a discussion of the show once it was over.

“And now, Act Four, Martha’s Vineyard,” he said, after applause for the performers.

“Shall we all put our lives in perspective now?” asked Dana Nunes, who sat at the table Friday. “Feels pretty damn good, doesn’t it?”

Next up for the Yard is a performance on Jan. 15 by the dance company Rubberband, in its first Island appearance, at the Martha’s Vineyard Performing Arts Center. For more information, visit dancetheyard.org.