[Mr.ac]

The sway bars don't look that bad, but it's far to easy for them to move like that. Maybe new sway bar bushing, or endlinks are in order. Have you hit any deep potholes lately? Or jumped a curb?

As far as the tires go, you always want the pair with the most thread on the rears.
That would keep the rear from getting that lose feeling.

Have you made sure you have the same tire pressure on all four? You might want to take it in to get an alignment recheck. If it's still not feeling right, the answer could be your tires are just worn out.