Keep in mind that any novel, story, play, or poem can have numerous thematic ideas working, and at one time, a reader can see several developing in tandem. With that in mind, I will offer an answer to your question with the caveat that I can suggest a central idea,...
Keep in mind that any novel, story, play, or poem can have numerous thematic ideas working, and at one time, a reader can see several developing in tandem. With that in mind, I will offer an answer to your question with the caveat that I can suggest a central idea, if not the central idea, because there isn't only one.
One of the biggest struggles faced by Yossarian is the desire to escape and the paradox that keeps him in the war. Heller invented the phrase catch-22, and it has become a standard expression of a paradoxically unsolvable problem. To over-simplify, the protagonist wishes to stop flying missions (he has served his assigned time but is being held through a constant revision of the required number of missions), but they tell him he can only stop flying missions if he proves to be physically or mentally incapable. He doesn't want to intentionally harm himself, and if he acts crazy to get out on mental grounds, he will be proving himself sane, because who but an insane man would want to keep flying missions?
As the novel progresses, a few patterns emerge. A particular mission, in which Snowden, a fellow soldier, dies in Yossarian's arms, is retold with increasingly vivid and disturbing detail; a con artist named Milo Minderbender creates an elaborate network of businesses that take advantage of the Air Force, the soldiers, and the locals; Yossarian repeatedly tries to find a way out and repeatedly fails; and the incompetence and brutality of the people that surround him increases until the soldiers and officers are raping and killing people in the local village and bombing their own squad to rack up more missions.
The novel is rich with detail, and the constant retelling of particular events builds layer after layer of meaning to be explored for ideas. A few important ideas the novel deals with are the effects of the trauma of war, the absurdity of authoritative order imposed on a chaotic situation, and the difficulty of making meaningful connections with other humans in an environment in which one will likely see them die. All of these relate to a larger issue that war stories often explore—the difficulty of remaining sane and civil when consciously trying to kill others.