On Saturday, March 29, Sanaa Sondhi’s short story “The Story of the Girls That Love to Dance and Love Each Other” was brought to life by 15 New York improv actors on a stage in the basement of the Drama Book Shop on West 40th Street in Manhattan. It was a sold-out show—about 60 people. Ms. Sondhi, the author, wore a yellow dress and sat in the front row. She was a little nervous. She had just turned 5 years old.

Standing in the back of theater, Jamie Salka—31, medium height, short brown hair, pointy nose, intense eyes with matching dark circles underneath—was grinning in a way that many of the youngsters in the audience might associate with a mad scientist. He is a lead producer and executive director for Story Pirates, a group that takes stories and plays written by little kids and acts them out—and sings them out—onstage. Sometimes they film the performances and the videos end up on YouTube. They also work with schools, hospitals and charities. In addition to their weekly Saturday matinees—which always include a couple of freshly adapted works from children in the audience—they’re big at birthday parties. Thanks to a gushing mention of Story Pirates by comedian Jon Stewart on Larry King’s show in February, they’re doing about 12 birthdays a month, charging between $650 and $2,000, depending on size.

Sanaa had completed her story only a few weeks ago, and submitted it via e-mail to the Story Pirates Web site. Her two-page manuscript begins simply enough: “There are two girls. There names are Sarina, and Sabrina and they are sisters and they love to have picnics outside. They have a lot of purses and they really do not know if there is a secret garden.” It follows that another of their sisters, named Flowerdash, is also looking for the secret garden. She has a dog she shares with her sisters, named Flower Rainbow. A journey ensues. “She also packed a heart bathing suit in her bag because she is also planning deep sea diving to see the Indian Mermaid.” Flowerdash pets various undersea creatures, even sharks—“They don’t bite her. And because she has her own American girl doll that is named Flower Cherry”—and discovers that the Indian Mermaid is also a whale mermaid. She then boards a plane with her parents and Flower Rainbow, and together they visit Florida, India, New Zealand and South Africa.

The adapted musical version—performed on a simple stage with a makeshift balcony from which various pirate and lurking puppets maintain a running commentary—essentially followed this plot line. A few nips and tucks, a few over-the-top jokes sprinkled in. The Story Pirate team heightened the competitive tension alluded to in Sanaa’s script by portraying Flowerdash on a quest to find the garden before her pesky sisters Sarina and Sabrina. A catchy theme song and some choreographed dances served as a transition between scenes.

The chorus of the song—“We love to Dance, and Dance, and Dance on the beach. Dance and Dance and Dance within reach of the water!”—came from a line in Sanaa’s story that reads, “She has three suit cases and she loves to dance and dance and dance on the beach.” (A similar strategy was employed in the adaptation of a tyke named Taylor’s poignant bed-wetting story, enigmatically titled “Ed.” )

A few years ago, Mr. Salka was working as one of theater and film producer Scott Rudin’s five assistants. Work began at six and often ended after midnight. He said Mr. Rudin’s “brutal” ways inspired a love of producing—and an awareness that working harder than everyone else, “wasn’t that hard of a challenge.”

HE STILL GETS up at six. Sometimes in the afternoon at the gym, he’ll speed-walk on a treadmill side by side with Lee Overtree, the artistic director and founding partner of Story Pirates, both of them gripping iPhones. Growing up in L.A., Mr. Salka had contemplated becoming a rabbi, but his love of theater got the best of him.

“When I worked for Scott [Rudin], I became convinced that you can be a brilliant producer, but you have to sell out your soul in order to work in Hollywood,” Mr. Salka said the other day over an iced skim caramel macchiato. “And I almost bought into that until I saw the Story Pirates.”

After basic training under Mr. Rudin, he took a similar gig working under Hollywood producer Jonathan Glickman in L.A. In the fall of 2003, he was back in New York. Some classmates from the Northwestern theater program invited him to the original production of Story Pirates at the Vital Theater. It was a hourlong show based on stories written by young children.

“I thought the show could be everywhere: I thought it could be a national tour, I thought it could be a national institution, with a sitting company in every city,” he said. “As a producer it made so much sense to me. But what I didn’t realize is how great the classes could be that we teach to kids, that it could be one of the best birthday parties in New York, that we could take the stories that kids write and publish them into books, which we would ultimately like to be doing, DVD’s of every show we do and sell them to people in the audience—it makes a lot of sense in almost every way.”

The first Story Pirates show at their own theater was a flop—all the actors’ friends turned out for the first two weeks and then there was no one in the audience. The problem was, between them—it began as nine pirates, now there are about 40—they didn’t know a single kid or parent. The plan had been to do the same show for three months, then change. Instead, they realized they needed to change the show every week in order to pack the house. The trick was to have a standard show but include a few new plays each week—the kids who wrote those plays would show up and bring their families.

Birthday parties were also a major turning point. “When you do a show, you have to sell 60 tickets; when you do a birthday party, you have to sell one family and they bring 60 people,” Mr. Salka explained.

“I realized that we had to deliver the best birthday party in the city,” he continued. “And I think that’s what we have, because we not only give people that show, which features Daily Show- or Saturday Night Live-quality talent for a 6-year-old’s party, but we also take care of every single detail of the party; we do the food the decorations, the party favors—the parents can walk in empty-handed and know that they’re going to get a unique party done for their kid, and we have done all the heavy lifting.”

It was one of these birthdays that brought the Story Pirates to Jon Stewart’s attention. In December, TV producer Dara-Lynn Kubovy-Weiss held a party for her son at the Chinatown Y.M.C.A. Eighty kids and tons of parents attended, including actor Billy Crudup and Mr. Stewart.

Mrs. Kubovy-Weiss had taken her kids Betty, 4, and Theo, now 3, to see the Story Pirates last summer. That night after the show, Betty was inspired to dictate four stories to Mrs. Kubovy-Weiss as she lay in bed trying to go to sleep. She called the Story Pirates the next day to schedule them to perform at Betty and Theo’s birthday party. “They somehow managed to transfer Betty and Theo’s collaboratively written, largely nonsensical story to a coherent sketch that stayed true to what they wrote,” Mrs. Kubovy-Weiss said.

Back to last Saturday: After the show ended, Sanaa—mom is a professor at Weill Cornell Medical College, dad is in finance, they live on the Upper West Side—said she was already busy working on a sequel. It will take place in Antarctica.

About two years ago, the Story Pirates added evening shows for adults. Free wine is provided.

“The reason we started doing the show for adults is because parents were loving it just as much as the kids,” said Mr. Overtree. “We’re doing the exact same show at 9 p.m. for 20- and 30-somethings that we did today for toddlers-through-fifth-graders and their families.” The evening show has sold out since its inception.

“Most people seem like—well, they find something that inspires them, so it really, I think, helps people find parts of the story that inspires them,” said Tatia Brensnahan, 8, who has written five plays so far. “They were definitely trying to get a TV show when I last saw them. I think that would be a good place for them to be.”