WordNet sense 1 (the team that has the ball (or puck) and is trying to score):

offence

WordNet sense 2 (a feeling of anger caused by being offended):

umbrage

WordNet sense 3 (a lack of politeness; a failure to show regard for others; wounding the feelings or others):

discourtesy, offensive activity

WordNet sense 4 (the action of attacking an enemy):

offensive

WordNet sense 5 (a crime less serious than a felony):

infraction, infringement, misdemeanor, violation, misdemeanour