Offense, resentment, umbrage, pique, dudgeon, huff are comparable when they mean a person's emotional reaction to what he regards as a slight, an affront, an insult, or an indignity.
Offense implies an often extreme state of displeasure or of wounded feelings.
Resentment implies more indignation than offense, more prolonged dwelling upon what one regards as a personal injury or grievance, and, often, more ill will to the person who has offended.
Umbrage, used chiefly in the phrase "to take umbrage," differs from offense in carrying a clearer implication of being slighted or unfairly ignored; the term therefore generally suggests ruffled pride, resentful suspicion of others' motives, or jealousy of those favored.
Very often umbrage is not clearly distinguishable from offense.
Pique applies to the reaction of one who has taken offense or umbrage, but it distinctively suggests a petty cause and a transient mood and often connotes wounded vanity.
Dudgeon applies chiefly to a fit of angry resentment or indignation provoked by opposition to one's views or a refusal of one's request.
Huff, like dudgeon, applies to a fit of anger, but it comes closer to pique in suggesting pettiness of cause and transitoriness; distinctively it implies petulance and a sulky refusal to have more to do with those who have offended.