Before entering the intimate space where the theater company Adjusted Realists is staging Stephen Kaliski’s “The Refugees,” audience members can peruse posters that lay out vexing moral dilemmas, both historical and hypothetical. In one, several people tied to train tracks can be saved by diverting an approaching train, but only if someone else is killed — possibly a beloved relative, in one of two bleak variations proposed.

It’s a sign that “Refugees” will not offer any pie-in-the-sky solutions to the enormous, and related, challenges it addresses. Using characters drawn from Greek mythology, Mr. Kaliski, who also directs the production, examines the increasingly inextricable link between immigration and climate change, and the role that privilege, or lack of it, plays in this connection.  

The setting is a fantastical Argos, which by some fluke of fortune has been spared from a series of natural disasters that have utterly devastated Athens, Minoa, and Thracia. As the queen, Clytemnestra, and her children, Electra and Orestes, enjoy temperature-controlled luxury in their palace, hordes of displaced foreigners huddle in camps outside the city gates.

Clytemnestra, played with droll imperiousness by Rachel McPhee, refuses them entry and seems unmoved by their plight, her greater concern being that neither her gay son nor her sickly daughter — this Electra suffers from some mysterious, enervating ailment — will produce a royal grandchild. Yet Orestes and Electra and their friends want to take in the unlucky travelers, and they lament the narrow-mindedness of their mother’s generation.

“Sometimes, when I speak in front of the older Argives, there’s this gnawing sense that they aren’t as jazzed as we are, like they suspect these new neighbors will drain rather than replenish,” Orestes, an alternately impish and excitable figure in Jonathan Nathan Dingle-El’s endearing performance, says. His lover, Pylades, played by a wry Matt Mastromatteo, reassures him that Clytemnestra will eventually be converted by “the conviction of the young asserting the world they want to inherit.”

If these lines seem almost comically simplistic and naïve, not to mention a little pompous, it’s because they’re meant to be. Although “Refugees” may sound like an earnest, even preachy exercise on paper, Mr. Kaliski — wielding a deft mix of skepticism and whimsy, without getting too flighty or cynical — portrays both the issues at hand and the people divided over them as maddeningly complicated. 

Notably, the playwright and director doesn’t idealize his idealists. Caroline Do’s smart, purposeful Electra may get fired up while scheming to trick her mother into a meeting with Athenian, Minoan, and Thracian representatives, but when a nurse who was herself displaced arrives to feed green smoothies to her, the pampered daughter barely acknowledges her presence. And when Clytemnestra agrees to finally visit the camps, some of the young Argyles who had been so eager to play rescuer suddenly worry that they will be, as one puts it, “incapacitated by charity.”

Those who earn our unconditional sympathy in “Refugees” are the title characters, of course, played by actors culled from the same chorus representing the Argyles. They emerge at first in a trickle of cameos, their greater abundance suggested by flickers of color visible behind a thick plastic curtain that’s prominent in Anita Tripathi’s spare set. The curtain eventually opens to disclose what could be described, without divulging too much, as remnants of lives left behind — and not voluntarily, or conveniently.

A planned series of short testimonials evolves into a more inclusive ceremony, in which catastrophes are described alongside lost pleasures, some of them literally as simple as pie, or chocolate ice cream. The spell is almost broken when a couple of speakers inexplicably begin singing ’80s rock anthems (they stop after a few bars), but the message — that a permanent home is something many people cannot take for granted — gets through.          

A final twist among several toward the end brings Mr. Kaliski’s imaginary world closer to our own, and there are direct appeals to the audience from the beginning, when attendees are asked to write a haiku inspired by four words: “I didn’t do enough.” It’s not an admonishment, but rather, like “Refugees” overall, a reminder that progress isn’t easy — any more than complacency is acceptable.