Angela’s Mixtape, through August 11 at the Martha’s Vineyard Playhouse, is a time-tripping, genre-blending and often very funny autobiography of its playwright, Eisa Davis, in her childhood and youth.

“We bounce back and forth in time,” Ms. Davis, played by Jules Latimer, tells the audience at the start of the show, which runs a lively 70 minutes and mixes music, rhymes and dance steps with its dialogue.

In life, as in her onstage character, Ms. Davis goes by her middle name. Her first is Angela, after her famous aunt Angela Davis, an activist and intellectual who was behind bars when her namesake came into the world.

The older Ms. Davis was jailed in 1970 following a months-long manhunt after her gun was used in a Marin County, Calif. courtroom shootout that left four people dead. After more than a year of imprisonment, she was acquitted of involvement in the crime and continues to teach and write.

Sarin Monae West plays Angela Davis — MJ Bruder Munafo

Her niece’s free-form memoir reveals Angela Davis as a complex, patient and loving woman.

“The Angela I knew used to blow-dry my hair and French braid it,” recalls Eisa onstage. “She made me mixtapes with Keith Jarrett and Billie Holiday.”

Angela, played by Sarin Monae West, also gives her niece combined lessons in Marxism and driving.

“This is harder than Marx,” protests the teen, referring to learning to drive.

“Philosophers have only interpreted the world,” retorts her aunt. “Now let’s see if you can put it into second gear.”

In another telling scene from earlier in Eisa’s life, Angela asks her young niece if she’s ever seen a yellow watermelon. “Watermelons are red!” Eisa insists, until her aunt cuts the melon open to reveal the yellow flesh.

The lesson: “What you expect and what you get aren’t always the same,” Angela tells her.

Much of the play traces Eisa’s story as she grows up in an activist family: her Berkeley childhood, the hippie neighbors, the frequent demonstrations. Played by April Armstrong, Eisa’s mother — Angela’s sister Fania — is relentlessly cheerful and tirelessly committed to “the struggle.”

“Every waking moment is for liberation,” she declares.

Proud of her sister’s activism, she

trains little Eisa to declaim passages from Angela’s writings. This is how we learn of Angela’s and Fania’s upbringing in racially violent “Bombingham,” Ala., during a sobering scene that enlists gospel music and verse to paint the picture: “Step right into our house on the hill—hate is the local specialty and we’re eating our fill.”

Jules Latimer and Erin Roch. — MJ Bruder Munafo

Ms. Latimer, a third-year student at Juilliard, is onstage throughout the play and gives a clear-eyed, honest performance that perfectly expresses little Eisa’s childhood confusion about why her aunt is so famous. She’s also terrific as the maturing girl, navigating social challenges at school, and as the questioning Harvard student who wonders if she’s living up to the name Angela Davis.

“You don’t have enough black friends” is one of her mother’s stock admonitions.

Meanwhile, the girls at school (played by the protean Erin Roche, who portrays several characters during the evening) are pestering Eisa to define her racial identity, “Are you mixed?” or putting her down, “You act like you’re rich.”

Ms. Roche is note-perfect throughout, whether she’s a schoolgirl snubbing a former friend or Toni Morrison sweeping in for dinner with Fania.

The widest range of characters, though, belongs to Nora Cole. In addition to her main role as Grandma, the

moral authority in the Davis family, Ms. Cole convincingly plays a white Birmingham shoe salesman, Eisa’s stepfather Larry and even former President Ronald Reagan.

Directed by Adrienne D. Williams, the fragmentary narrative flows from one scene to the next as naturally as a stream of memories. Ms. Williams directed Crumbs from the Table of Joy by Lynn Nottage, during the 2016 playhouse season.

Angela’s Mixtape plays Tuesday through Saturday through August 11. Visit mvplayhouse.org.