Source : Webster's Revised Unabridged Dictionary (1913)

Incongruous \In*con"gru*ous\, a. [L. incongruus. See {In-} not,
   and {Congruous}.]
   Not congruous; reciprocally disagreeing; not capable of
   harmonizing or readily assimilating; inharmonious;
   inappropriate; unsuitable; not fitting; inconsistent;
   improper; as, an incongruous remark; incongruous behavior,
   action, dress, etc. ``Incongruous mixtures of opinions.''
   --I. Taylor. ``Made up of incongruous parts.'' --Macaulay.

         Incongruous denotes that kind of absence of harmony or
         suitableness of which the taste and experience of men
         takes cognizance.                        --C. J. Smith.

   {Incongruous numbers} (Arith.), two numbers, which, with
      respect to a third, are such that their difference can not
      be divided by it without a remainder, the two numbers
      being said to be incongruous with respect to the third;
      as, twenty-five are incongruous with respect to four.

   Syn: Inconsistent; unsuitable; inharmonious; disagreeing;
        absurd; inappropriate; unfit; improper. See
        {Inconsistent}. -- {In*con"gru*ous*ly}, adv. --
        {In*con"gru*ous*ness}, n.

Source : WordNet®

incongruously
     adv : in an incongruous manner; "his shirttails stuck out from his
           tuxedo pants somewhat incongruously"