Wow! They mean the same (not in harmony, or agreement, discord, etc), but as a native English speaker from the states, I can tell you that you will probably will never hear the words inharmony or inharmoniousness used. I won't say Never, 'probably never' is pretty certain.

Inharmony and disharmony mean exactly the same thing. The prefixes "dis", and "in" both mean the same thing. Disharmony is the more common word. I have never seen inharmoniousness before in my life.