Mountain bike rear wheel tilts after remounting Backstory: Total newbie regarding repairing cycles and the proper cycling terminology, so please take that into account.

Actual story: 

I had a fall and the rear wheel started touching the brakes (non-disc), so I took it out aiming to remount it and as a final result I broke the quick release.

After a long walk home, went and bought a new quick release (the wheel has some nuts to some effect I'm not 100% sure about). I installed it according to this video (and also followed the "tight enough to leave a mark on the hand, but no tighter" rule I read about somewhere), seemingly aligned (in the middle between the frame). Now, I see two things:


The wheel tilts sideways about 1/4" or a bit more, it's not fixed.
When under load the wheel ends up either touching the brakes or directly the frame.


Thus I think that I'm either misinstalling the wheel, or that after the fall something else got broken or damaged.

The actual question is, how to find the actual problem (misinstalling the wheel or something else, or both) and its solution?

EDIT: Here's a video of how the wheel tilts, and another video of a possible culprit (damaged spoke). Could that damage explain the amount of tilting?
It could be some spokes or the rim got damaged. You should try touching them to see if any is broken. If they are loose you should tighten them to align the rim. If you can't do it yourself a bike shop will do it for you easily. Broken spokes can be changed.