I have sound-activated neon lights and a blacklight in the interior of
my car. In which states is it legal to drive with these lights turned
on?

I believe it is actually legal everywhere that doesn't specifically
have a law against it.

Hmmm.. so it may be good to rephrase the question. In what states is
it illegal to drive with these types of lights turned on?

To the best of my knowledge it is illegal in almost every state.  I
know in Wisconsin (where I live) you cannot have any lights on in the
interior, I found out the hard way.  You can however get away with it
if it can't be seen from the outside, i.e. pedal lights or dim lights.
 I have been told about three times that I can't drive with them on. 
You can have them on if your parked though for sure, unless their blue
(atleast in wisconsin) then you have to be 75+ feet away from the road
with blue lights on.  Also red lights cannot be visable infront of the
cab (front door on a car.  Hope that helps ya some.