Michael Glenn as Jack and Susan Rome as Kate in Neil Simon’s “Brighton Beach Memoirs” at Theater J through May 7. (Teresa Wood)

You don’t want to get between Kate Jerome and any throw pillow she may be plumping. When this Brooklyn homemaker tidies, she doesn’t content herself with merely shaking or squeezing the sofa cushions into dent-free shape: She drives a knee into them, moving with quick, impatient energy, her face drawn tight with exasperation and worry.

Susan Rome’s portrait of the harried, controlling Kate is an ­invaluable anchoring force in ­director Matt Torney’s production of “Brighton Beach Memoirs” at Theater J. Few of the other actors embed their characters quite as deeply and seamlessly in the world of Neil Simon’s semiautobiographical play, about a cash-strapped household in 1937 Brooklyn. Still, it’s a pleasant production, well stocked with funny, absorbing moments and boasting a couple of notably persuasive turns by young actors.

Cole Sitilides, center, plays 15-year-old Eugene in Theater J’s “Brighton Beach Memoirs.” (Teresa Wood)

One of those youthful performers is Cole Sitilides, who embodies the play’s central character: 15-year-old Eugene, who periodically comments — with precocious and sometimes wisecracking sagacity — on the action. Obsessed with the Yankees and, increasingly, girls, Eugene tangles regularly with his mother, Kate, who doesn’t appreciate his quips. Her attitude isn’t surprising: Tensions are running high in the household, which has taken in Kate’s fragile widowed sister, Blanche, and her daughters, requiring Eugene’s father, Jack, to work two jobs to make ends meet.

The stressed-out adults sometimes give Eugene the short end of the stick, at least in his opinion. “Guess who’s going to get blamed for the war in Europe?” he deadpans to the audience after his parents scold him for touching the radio before a newscast.

Whatever Eugene is spouting off about, the self-possessed ­Sitilides divertingly channels his smart-alecky energy. Also very good is Marie-Josée Bourelly, who exudes verve and rebelliousness as Blanche’s headstrong older adolescent daughter, Nora — a figure of fascination to Eugene, who pines to know more about female anatomy.

Nora (Marie-Josée Bourelly) shares big news with her family (from left: Lise Bruneau, Cole Sitilides, Sarah Kathryn Makl and Susan Rome) in a scene from “Brighton Beach Memoirs.” (Teresa Wood)

In other roles, Eli Pendry conveys the sincerity and callowness of Stanley, Eugene’s mishap-prone older brother. (Sitilides, Bourelly, Pendry and Sarah Kathryn Makl, who plays Blanche’s mollycoddled younger daughter, are all local teenage actors.) Lise Bruneau is aptly wistful and fluttery as Blanche, whose planned date with a neighbor provokes one of the household’s many crises, and Michael Glenn registers the weariness of Jack.

Suitably packed with ­Depression-era decor and clutter, Luciana Stecconi’s domestic set lends the tale added atmosphere and a sense of rootedness. You can even see the wear in the center of the steps that lead to the home’s second story. Ivania Stack’s period costumes (think knickers and baseball cap for Eugene) enhance the specificity.

“Brighton Beach Memoirs” has sober dramatic moments, including allusions to grim events in 1930s Europe. A topic of occasional discussion for Eugene’s family is the fate of their European relatives, who may wind up in Brooklyn as refugees. That plot point carries an added wallop of poignancy, given the current refugee crisis.

Despite the shadows, Eugene’s unmistakable talent (if he can’t be a professional baseball player, he wants to be a writer) and humor keep the tale upbeat. So does the obvious strength of his family’s bond: It’s love that drives Kate to plump those cushions so fiercely.

Brighton Beach Memoirs, by Neil Simon. Directed by Matt Torney; lighting design, Colin K. Bills; sound, James Bigbee Garver; properties, Timothy J. Jones. About 2 hours and 30 minutes. Through May 7 at Theater J, 1529 16th St. NW. Tickets: $15-$57. Call 202-777-3210 or visit theaterj.org.