As in all plays, the characters in Angels are defined by their actions. In Perestroika, Harper's constant escapes into fantasy reveal her inability to cope with reality, but her rejection of Joe shows that she ultimately finds inner strength. Similarly, Prior spends most of his time running from the task the angel gave him. In the end, though, he wrestles the angel, goes to Heaven, and forces her and the other angels to take back the book. Like Harper, Prior's final actions show the strength he has gained over the course of the play.
Many of the characters in the play are at least partly defined by their sexual preferences. Roy is ashamed that he's gay, and he stays in the closet even on his deathbed. Joe is out of the closet by the time Part Two rolls around, and he begins a sexual relationship with Louis. Over the course of the play, he seems to come to terms with his homosexuality in some ways, which makes it all the more painful when Louis turns on him for being too conservative. Prior and Belize are the other two gay men in the play; like the others, they struggle with acceptance in an intolerant time.
Then of course there's Harper, who has the misfortune of being married to and in love with a gay man. Late in the play, the two have reunion sex, but it doesn't go too well. Joe keeps his eyes closed the whole time (like usual), and afterwards he admits that he was imagining a man (ouch). Harper's sexual frustration is an underlying tension for her character throughout the play.
Kushner's stage directions give us some helpful tips for understanding the characters. For example, we're told that Roy is an "unofficial power broker," that Prior "lives very modestly but with great style off a small trust fund," and that Belize's real name is "Norman Arriaga; Belize is a drag name that stuck."