It sounds like your teacher might be asking you to perform a psychological evaluation of each. Are there any outside sources you are supposed to use? Are you supposed to be diagnosing the men with specific issues, or just using your own frame of reference?
If you are not supposed to use any outside sources, you can analyze each man using these questions:
Does the character seem to have any "issues"? Does he display any behavior that concerns you? Interests you? For example, I find George's treatment of Lennie to be both interesting and disturbing. George clearly cares about Lennie, but is very impatient with hem.
What seems to motivate the character? What needs/desires make him act the way he does? For example, why is Lennie so obsessed with petting soft things?
Has anything in the man's environment affected him psychologically? For example, you might consider how Slim has been affected psychologically by the life of a migrant worker (the lack of permanence, etc).