Compunction is similar to an obligation; if you are "under compunction," then you are bound by some debt or sentence to do something. Repentance is actually an action rather than a feeling or condition: it is an act of the will which disowns whatever behavior you regret, and to repent implies a determination not to make the same mistake again. Contrition is the expressed emotion of being sorry for something; if you went to a person you had wronged, to make amends and ask their forgiveness, you would be "contrite" toward them. Remorse is simply another word for regret - you feel bad within yourself, either for what you did or for how the consequences affected you.