Sit yourself down to a stunning, sensory-overloading immersion in the refugee experience. Joe Murphy and Joe Robertson’s kaleidoscopic play, directed by Stephen Daldry and Justin Martin, finally reaches Washington, in a co-production for Shakespeare Theatre Company and Woolly Mammoth Theatre that originated in London and then ran in New York. The audience is divided into national groups, as if we, too, are denizens of a camp for migrants in Calais, France — a device modeled on actual events. Over the course of nearly three hours, the stories of those trapped in international limbo unfold, with the dramatizing of all the attendant outrages and heartbreak.