The Collaborative International Dictionary of English v.0.48:

Offensive \Of*fen"sive\, a. [Cf. F. offensif. See Offend.]
   [1913 Webster]
   1. Giving offense; causing displeasure or resentment;
      displeasing; annoying; as, offensive words.
      [1913 Webster]

   2. Giving pain or unpleasant sensations; disagreeable;
      revolting; noxious; as, an offensive smell; offensive
      sounds. "Offensive to the stomach." --Bacon.
      [1913 Webster]

   3. Making the first attack; assailant; aggressive; hence,
      used in attacking; -- opposed to defensive; as, an
      offensive war; offensive weapons.
      [1913 Webster]

   League offensive and defensive, a leaque that requires all
      the parties to it to make war together against any foe,
      and to defend one another if attacked.
      [1913 Webster]

   Syn: Displeasing; disagreeable; distasteful; obnoxious;
        abhorrent; disgusting; impertinent; rude; saucy;
        reproachful; opprobrious; insulting; insolent; abusive;
        scurrilous; assailant; attacking; invading.
        [1913 Webster] -- Of*fen"sive*ly, adv. --
        Of*fen"sive*ness, n.
        [1913 Webster]

WordNet (r) 3.0 (2006):

offensively
    adv 1: in an unpleasantly offensive manner; "he smelled
           offensively unwashed" [ant: inoffensively]
    2: in an obnoxious manner; "he said so in one of his more
       offensively intellectually arrogant sentences" [syn:
       offensively, objectionably, obnoxiously]
    3: in an aggressive manner; "`In this crisis, we must act
       offensively,' the President said"; "the admiral intends to
       act offensively in the Mediterranean" [ant: defensively]