Well, thinking through the areas that you have identified should give you lots of ideas for how to answer your own question. However, just to briefly outline the main thematic elements of this excellent novel, it seems to me that there are at least three elements that you can talk about: family and belonging, identity, and class.
The various Greasers in many ways lack a traditional family. Ponyboy is looked after by his two elder brothers and Johnny, for example, has parents that are at best indifferent. Against this backdrop of absent or indifferent parents, the boys form their own "family" and show incredible loyalty towards their friends. Consider how the brothers make peace at the end of the novel, realising that "if we don't have each other, we don't have anything." This presents a message of hope against the backdrop of other realities, such as violence and class.
Concerning identity, this is a novel about the narrator who "finds himself" during its pages. Towards the end of the novel, after experiencing the death of Johnny and so much else, we get a sense that Ponyboy has sorted through the bewildering number of different role models and examples, good and bad, and has determined to work hard and go to college like Darry wants him to. His decision to document his story as part of his assignment shows considerable maturity and reflection.
Lastly, throughout the novel, it is impossible to ignore the issues of class that cruelly divide youth into one of two opposing camps: the Greasers and the Socs. Whilst the author outlines the differences between the two rival groups, no attempt is made to try to bridge the divide. Class distinctions are presented as an inevitable and unchangeable part of life. The only hope that is available is that at least both sides can move towards understanding each other. Consider how this happens between Cherry and Randy. At the end of Chapter Seven note what Ponyboy says after his chat with Randy:
Socs were just guys after all. Things were rough all over, but it was better that way. That way you could tell the other guy was human too.
Through his talks with Randy and Cherry, Ponyboy goes beyond simply seeing the Socs as "the enemy" and realises that they are just boys like him, human and vulnerable. Lastly, his decision to write his story is to help the "Hundreds of boys who maybe watched sunsets and looked at stars and ached for something better." Although there is no hard and fast plan for reconciliation between the classes, Ponyboy concludes that mutual understanding of each other's humanity is a good place to start.