The sad souls in Melissa James Gibson’s new play, “What Rhymes With America,” wear their dissatisfaction in different styles. For the divorced dad trying to strengthen his bond with his teenage daughter, it’s like a drab overcoat he cannot manage to shrug off. For the 40-something virgin whose father has just died, shrouding herself in singlehood has almost become a comfort, like a big puffy coat. The would-be actress stuck working as an extra in an opera puts on a braver front: wielding her anger as a Valkyrie does her armor.

Those are, as it happens, among the costumes worn by the characters in this touching, sorrowful comedy, which opened Wednesday night at the Atlantic Theater Company’s Linda Gross Theater in a production directed by Daniel Aukin. But what the characters wear is much less important than what they say and how they say it. Language may sow more confusion than connection in the distinctive worlds conjured by Ms. Gibson, author of the terrific comedy-drama “This,” but it’s about all her wandering souls have left to cling to.

Although she deploys words with an entrancing oddity, Ms. Gibson clearly shares her characters’ anxiety about their seeming inadequacy. Sometimes they come tumbling forth in rippling streams; sometimes they falter and stick, and have to be yanked out with no rhythm or rhyme. All too rarely do they succeed in bringing people together, or even keeping them from growing apart.

In the opening scene the unhappy father, Hank (Chris Bauer), cannot even manage to persuade his 16-year-old daughter, Marlene (Aimee Carrero), to open the front door to say hello. An economist who lost his research grants, Hank tried to make up the difference with his wife’s money — hence her insistence that Marlene keep clear of her father. But Marlene is willing to bend the rules. As Hank tries to keep up a steady stream of father-daughter chitchat, she sits just inside the door listening as he stands outside. (The piteousness of their intimate distance is enhanced by the absence of an actual door, in the simple set design of Laura Jellinek.)