Oxymoronic soundtrack — mismatch audio to visuals

Solution 1:

Perhaps the best phrase / word to describe two juxtaposed circumstances that are ridiculously discordant is (totally) incongruous.

Solution 2:

How about dissonance? It conjures up the appropriate sense of 'ick' and 'what the heck??!' in my head from having music that's got a completely opposite emotional timbre to the video footage.

Solution 3:

@Edwin's "incongruous" is good, but maybe a bit stuffy. How about just:

Inappropriate

not appropriate; not proper or suitable: an inappropriate dress for the occasion.

Others:

Unfitting, unsuitable, silly, inept, irreverent, idiotic, misunderstood, over-stylized, hipster, or this.

You can really express your opinion on their misuse, vs. just implying that it is "not working for you".

Solution 4:

lip-flap
Wikipedia entry on Audio to video synchronization lists two terms for the lack of it: lip sync error, lip-flap.

See also:
Experts' Experts: Lip-Flap — Why your expensive TV's audio and video are out of sync

For an adjective, you would in all possibility, use
(A/V) unsynced