Steering shakes, Car pulls to the right and Noisy..

The steering wheel in my 96 sentra shakes when I let go of it. Not majorly, but good enough for me to notice the shake. I am thinking that this may not be a serious problem coz I have noticed this in my friend's 97 Galant too. However, I would like to fix this 'shaking' if it doesn't take much to do it. Also, when I let go of the wheel, the car pulls to the right. Could these be related?

Also, when I got this car, it drove quiet..but these days it's gotten noisy..It's not terrible, but I have riden other sentra's and I believe they were quieter than mine.. The car is still under (used) warranty..but I wanted to ask everyone here before I decided to take it in to the dealer for what I think may be non-critical problems. Thanks.

tires worn? that's what it sounds like, check that tread.