Adverbial has 3 senses

• offensively(r = adv.all) - in an unpleasantly offensive manner; "he smelled offensively unwashed"
Antonym: inoffensively

• offensively(r = adv.all) objectionably, obnoxiously - in an obnoxious manner; "he said so in one of his more offensively intellectually arrogant sentences"
• offensively(r = adv.all) - in an aggressive manner; "the admiral intends to act offensively in the Mediterranean"; "`In this crisis, we must act offensively,' the President said"
Antonym: defensively