This is man vs. man because the Soc's and the Greasers have a big rivalry. The fight they had the Greasers had a passion for and so did some of the Soc's. The Greasers won for Johnny.
This conflict is man vs. self because Ponyboy is caught in his own thoughts. He is concerned about Johnny's health, being jumped again, and trying to be friendly with Darry. Now he's even worse because he has to overcome his own sadness at the lost of Johnny.
Ponyboy has a conflict with the church on fire because the church is where he and Johhny had stayed for awhile and he cared about it.