The Question and Answer section for The Birthday Party is a great resource to ask questions, find answers, and discuss the novel.
I think that Stanley loses whatever power he might have had during the play. His aggressive depression transitions into a nervous breakdown when Goldberg and McCann arrive, until he is nothing but a bumbling idiot in Act III.
Petey and Meg have a complacent marriage. Neither of them is completely happy, but they're both happy to leave things as they are.
Peter lies because he knows that the knowledge Stanley has been taken away will ultimtely leave Meg as mentally fragile as Stanley.