There are a variety of emotions featured in Hinton's work. One emotion would be the need to belong. The Greasers realize, to a large extent, that they are there for one another and that there is little else in the world to which they can link themselves other than one another. Another specific emotion which is present is the sense of resentment at all the social opportunities that the Socs afford, sometimes at the cost of the Greasers. There is a sense of sadness and self- destruction associated with Dally, confirmed with Johnny's death. In the voice of Ponyboy, there is a certain emotional growth and arc of maturation which allows for reflection and thought, contributing to a variety of emotions in his frame of reference.
This story has a lot of different emotions. I would say that the most important one is Ponyboy's yearning to improve himself, but I'm not sure what you would call that emotion.
A lot of the story revolves around the love that the Curtis boys feel for each other. I suppose you could also talk about the love between the various members of the Greasers, but the most important love is between the Curtis brothers. We see love motivate Darry to take care of the other two and we see their love develop (even though there are rough spots along the way).
Another major emotion is sorrow. I think that Johnny is a pretty sad character all along, and his death definitely brings sorrow into the story. So does Bob's death, since we see how much it affects Cherry.
But to me, the main emotion in the story is Ponyboy's desire to be something other than a hood. It is his desire to "stay gold." Throughout the story, we see him struggle with this desire and I think that is what the story is really about.
When I think of the characters in the book "The Outsiders" I am able to relate different emotions with different characters. Johnny has feelings of loneliness and abandonment. He has low self-esteem. He is also timid.
Dallas Winston, Dally, is angry. He has lost the ability to cope with life in any other manner than anger.
Darry, the oldest brother, is frustrated and angry. He has had to accept the responsibility of getting his brother through school and keeping the family together.
Two-Bit has the emotion of joy and laughter. He is a wise cracker but he enjoys being happy and making others happy.
Soda Pop is sensitive and in love with a girl. He worries bout his family and friends and tries to play mediator.
Bob, the Soc, is angry and spiteful.
Pony Boy has a need or desire to be something better than his circumstances. He loves the people he is around but he is more aware of the life beyond his upbringing. He is confused.