"Of," for the purposes of this discussion, means "about" or concerning; theater that is of the community is about the community. "By" means through the agency of; theater that is by the community is created (storied, written, performed and produced) by the community members themselves. "For" means in the presence of and in support of a previously constituted community. I have added the second phrase, "in support of," to denote social responsibility.
Dunno. This seems a little chaotic...