Person vs. Self: The novel focuses mainly on person vs. self conflict because it is a "coming-of-age" tale about Holling Hoodhood. As a seventh grader, Holling is in an awkward stage in life naturally, but to complicate matters, he does not fit in at school because he is neither Catholic or Jewish like the other students at his school. This causes him to be isolated every Wednesday. In the end, however, Holling discovers who he really is, what he likes and dislikes, and that he is not simply an "ordinary" boy. He is at peace with himself by the novel's conclusion. Man v. self conflict is the most signficant form of conflict in the novel, but I've listed some other examples of conflict below.
Person vs. Person: The primary "man v. man" conflict of the novel originally occurs between Holling and Mrs. Baker. However, as their relationship changes and becomes a mentor/apprentice one, Holling encounters conflict with his family, Meryl Lee, and several others--but nothing like the original "war" between Mrs. Baker and him.
Society: While Holling endures his own inner conflict, the world around him (society) is immersed in conflict. During the novel's course, the Vietnam War rages, MLK is assassinated, and Bobby Kennedy is killed. Gary Schmidt demonstrates that an individual can develop his own sense of self even if society is at war with itself.
Nature: There really is not much man v. nature conflict in the novel. You could perhaps list the incident with the rats and Holling's "race" with them as an example.
Unknown: Mrs. Baker certainly faces conflict with the unknown. During the novel, her husband is overseas in Vietnam. She receives word that he is missing in action and must deal with not knowing if he is still alive, if he is okay, and if she will ever see him again. In the end, she does hear from him, and the novel closes with her going to welcome him home.