This question is pretty broad. Allow me to answer part of it, and refer you to the links below for complete descriptions of the characters you've mentioned.
Greasers are typically from "the wrong side of the tracks." They are poor, and their social standing is one that demonstrates the "poor but proud" mentality. They wear grease in their hair, partially by choice, partially from lack of hygiene.
In contrast, socs are usually considered the rich kids. They are given cars for their sixteenth birthday, and have all the advantages of an affluent upbringing. With this in mind, it only stands to reason that there is conflict between greasers and socs.
For complete descriptions of each of the characters you have mentioned above, please visit the link below.