First, bearing play that goes away when the wheel is clamped in place is expected (see Sheldon Browns web-site for explanation). The smoothness thing could just mean your bearings need to be cleaned and replaced (if it's not a sealed unit). They would have to be in very bad shape to cause that much noise, but it's an easy thing to check (again, if it's not a sealed unit).
Don't know what's wrong, you didn't give us much to go on. Sideways movement of the cassette is a problem. If that puppy won't tighten down, something is hosed.
If it will tighten down, but the noise remains, you need to do some investigation. I'd start by doing some experiments to narrow down possible causes. Do you get the clicking/scratching noise in all gears? In fact, does it continue when you coast (don't pedal)? What about when spin the wheel and you aren't on the bike at all? If something hit your bike that hard, it may have messed up something in the drivetrain, maybe even bent the frame?