drivetrain problem

my 98 aurora with 160,000 miles on it. when you shift from park to reverse or reverse to drive it seems to be shifting awfall hard. like a loud clunking sound under car. also noticed when i put it in park and let off the brake the car seems to still move some distance before it stops. car also seems to vibrate some only under acceleration. you let off the gas it is fine. could all of these things be related to one problem???:screwy:

Many things can cause this motor/tranas mounts, axle joints, realistically someone has to drive this to do a proper diagnosis.