offensively has 2 distinct synonyms spread across 1 of its 3 senses. Each sense below keeps its own list, because a synonym belongs to a meaning and not to a word: swapping one sense's substitute into another sense's sentence is how a thesaurus makes writing worse. Its 2 recorded opposites are inoffensively, defensively.
Counts are distinct word forms across every sense. A synonym that appears under three senses is counted once here and shown three times below, under each sense it belongs to.
in an unpleasantly offensive manner
“he smelled offensively unwashed”
in an obnoxious manner
“he said so in one of his more offensively intellectually arrogant sentences”
in an aggressive manner
“`In this crisis, we must act offensively,' the President said”
Synonyms, antonyms and the broader and narrower relations for offensively come from Princeton University’s WordNet. Full sources and licences.