Decline, refuse, reject, repudiate, spurn are comparable when they mean to turn away something or someone by not consenting to accept, receive, or consider it or him.
Decline is the most courteous of these terms and is used chiefly in respect to invitations, offers (as of help), or services.
Refuse is more positive, often implying decisiveness, even ungraciousness.
Refuse, however, may imply, as decline does not, the denial of something expected or asked for.
Reject stresses a throwing away, a discarding, or abandoning; it implies a refusal to have anything to do with a person or thing.
Repudiate implies a casting off (as of a wife whom one refuses any longer to recognize or accept); it usually connotes either a disowning or a rejection with scorn as untrue, unauthorized, or unworthy of acceptance.
Spurn carries an even stronger implication of disdain or contempt in rejection than repudiate.