To me, "honor" is... Well, I guess I'd describe it as the good morals within someone, something to be protected and fought for. It's different than "duty," which I think is more an obligation to oneself and one's country and not necessarily something from the heart.

"Loyalty," though... I think of "loyalty" as an attachment, swearing one's self to something and sticking by it no matter what. I never gave thought to living "honorably," but I'm sure that'd involve staying true to yourself, honest and just. Not running away from a fight, but not starting one, either.

Why do you ask?