Third Person (Limited Omniscient)
Most of the book is focused on Yossarian. We know what he knows, which is a lot. There are some exceptions because Yossarian seems to have access to some of the other characters' knowledge – like the chaplain. Since each of the chapters introduces a new character, we sometimes see through that character's eyes. For example, we learn the background stories of the chaplain, Milo, and Major Major. So it's not quite a cut-and-dry third person limited. Like much of Catch-22, traditional categories are questioned here.