Character Roles
Protagonist
Ponyboy Curtis
Not only is Ponyboy our narrator, but he's the star of the show. Sure, he's focused on writing about his environment, but he's showing it to us through his own eyes instead of trying to represent the perspective of one of the other characters. And it's Ponyboy that we see grow and change through the course of the novel.
Antagonist
The Socials
To say that all Socials are antagonists would be an oversimplification. "Social" (in this novel) seems to refer to people like Cherry and Marcia as much as the boys who aren't involved in the violence and bullying. It also refers to the people (like Bob) who antagonize our protagonist, Ponyboy, and his friends. Socials as antagonists might also refer to people who use wealth, power, and privilege to gain unfair advantage or power over others.
Foil
Johnny Cade and Dallas Winston
Johnny and Dallas are foils for each other in their similarities and their differences. Throughout the novel we can find parallels between the two, although they're almost polar opposites in some ways. Johnny can stand up to Dallas in a way that nobody else would dare. Dallas treats Johnny with the utmost kindness, and handles most others roughly at best. These two bring out the best in each other, in those respects.
Johnny is timid and fearful on the outside but brave and heroic on the inside, mustering his courage when circumstances demand it. Dallas is fearless on the outside but shies away from helping others. He's willing to risk his life for crime but not to help, because he feels like all of society has let him down and deserves only the same from him. Johnny has been hurt badly by life as well, but he sees helping others as the way to save himself. In a tragic similarity, Johnny and Dally both die in this novel – Johnny in the process of helping others, Dally in a hopeless frenzy of rage and grief.
Muse
Johnny Cade, Dallas Winston, and Robert Sheldon
According to Encyclopedia Mythica, "The Greek goddesses who presided over the arts and sciences. They were believed to inspire all artists, especially poets, philosophers, and musicians" (source). Generally speaking, a muse is any person who inspires a creative work. At the end of The Outsiders, before he begins to write, Pony tells us about his inspiration to pick up the pen:
Remembering a handsome dark boy with a reckless grin and a hot temper [Bob]. A tough […] boy with a cigarette in his mouth and a bitter grin on his hard face [Dally]. Remembering […] a quiet, defeated looking sixteen-year-old […] [Johnny]. One week had taken all three of them. And I decided I could tell people. (12.71)
Although Pony has very different feeling for all three boys and had very different experiences with each of them, they do come together to inspire him to tell his story, and in a rather creative way.