Questions of identity and responsibility lie at the heart of Quiara Alegria Hudes’ “The Happiest Song Plays Last,” which opened Friday at The Actors Group in a stimulating, entertaining production of a thought-provoking and often difficult play.

It is the last in a trilogy that began with “Elliot, A Soldier’s Fugue,” followed by “Water by the Spoonful,” which won the 2012 Pulitzer Prize for Drama and was produced by TAG last year; Hudes also won the 2008 Tony Award for best musical for “In the Heights,” which she co-wrote with Lin-Manuel Miranda.

Set in the kingdom of Jordan, Philadelphia and cyberspace, where its young lead characters connect via Skype and texts, “Song” continues the saga of Elliot (drawn with taut sensitivity by Brandon Caban), a troubled Iraqi war vet, and his cousin Yaz (in a radiant, charismatic portrayal by Becky McGarvey), a professor of music, who have been close friends since childhood.

Enacting a scene in a film about the Iraq War that is being shot in Jordan, an explosion flings Shar (the engaging Victoria Brown Wilson) through the air to the ground in her black hijab before Elliot, in military fatigues, threatens her with a rifle. Elliot, an aspiring actor and former Marine, was hired as a military consultant on the film but in a lucky break has replaced the male lead; Shar, a Juilliard-trained actor from Beverly Hills is “one-quarter Egyptian, one-quarter Iranian, with Cherokee, Korean and WASP thrown in for flavor.”

The barrio-raised Elliot mocks Shar’s “Yale” education (actually, it is Yaz who went there) and tries to impress her with a list of the commercials he’s done, but his mood ricochets between sunny and withdrawn. For instance, Shar and Ali (the appealing Paul Yau), an Iraqi refugee and the film’s cultural consultant, saw him digging frantically in the dirt the night of his arrival. Elliot, haunted by his killing of an Iraqi civilian, is trying to literally bury the past.

Filled with admiration for the pro-democracy demonstrators of the Arab Spring, he talks Shar into going with him to Egypt.

Back in Philly, Yaz, too, is seeking a kind of redemption, although in her case it’s by returning to the past. She has sold her luxury condo and moved back to the old neighborhood, buying the house of her and Elliot’s beloved, community-nurturing aunt.

Yaz keeps her door unlocked, feeds the neighbors and employs the homeless Lefty (an affecting James Roberts), who calls her “Mom,” as he did her aunt. She is attracted by Augustin (David Greene in his TAG debut), a fellow teacher, musician and Puerto Rican political activist, and when she confides this to Elliot via Skype, he advises her to ditch her “granny panties” — and, indeed, she purchases her first thong.

Given the many political themes — from America’s role in the Middle East to the bombing of Vieques, Puerto Rico, homelessness, racism and inadequate medical care — that clutter this ambitious, often scattered work, it is no small feat to portray convincing, well-rounded characters and make sense of their largely internal conflicts. But thanks to understated, naturalistic acting and smart, subtle directing by Peggy Anne Siegmund, who also directed “Water” at TAG, we perceive and care for these characters as flawed but entire human beings rather than the stereotypes they could all too easily seem.

In one wonderful scene, Augustin tells Yaz about a spooky jam session he attended in a cantina on the slopes of a Puerto Rican volcano. Music, dirt and water — the many underground streams that flow below Philadelphia and sometimes bubble up — provide compelling metaphors throughout the play. A trio, the Latin Amigos, provides live Puerto Rican music, as well.

Hudes has said that each play in her trilogy is a stand-alone, but in this case, it doesn’t fully work. Still, TAG’s production is very much worth seeing. It resonates with the audience long after the curtain falls.