could be an old/worn balancer, crushed motor mounts, and/or bad tranny mount.... or a rotating part needs to be balanced, the driveshaft comes to mind, also check the ujoints and that its secured on to the rear end.... as for whining, check the fluid before you melt some gears....
Good solid suggestions but also remember that a certain amount of shifter vibration is normal if the rubber/foam donut isolators have been taken out of the shifter! I took mine out when I put in my Hurst shifter cuase I hated that rubery feeling in the shifter and can live with a little vibration at certain high rpm's!