Distorting video with live sound
There are several programs available that allow you to do that.
One very popular tool in the live visual industry is MAX (especially Max for Live).
Its a visual programming language to create visuals for live performances that also integrates into a few tools like Ableton Live.

A program that I personally use at work is called vvvv, its a visual programming tool aswell that allows for very complex programs and is more "multipurpose" than MAX and offers a huge collection of add-ons to work with all kinds of peripherals and input devices.
For getting started I highly recommend having a look at this cheat sheet, vvvv has a VERY minimalistic GUI and heavily relies on shortcuts and hidden menus for more advanced settings and features.

Unfortunately only available for Windows but unlike Max its absolutely free to use unless you want to use it commercially, then you have to buy a commercial license (no differnces to the free version, you still just download the same version but have permission to earn money with it).

A also a free solution but only available on Mac would be Quartz Composer which is coming with Xcode. Its also a visual programming language that works in a similar fashion like vvvv and MAX.

E: Another solution would be MadMapper, its more meant for projection mapping but also does video with filters that can react to sound. In can also integrate into Live afaik.