Check for bad U-joints. They can cause the vehicle to vibrate at certain speeds. Also, look at the harmonic balancer. Look for cracks in the rubber part.
It probably has a demon in it. from your description, it's probably a spawn of Beelzebub, which are often quite difficult to exercise. You probably will want to talk to your local pastor, or any church official in your vicinity, and get it expelled immediately. the effects you are experiencing now are light compared to down the road. (no pun intended)
Your tires might be out of balance. You might have a broken cord in a tire. You might have worn components in your front suspension or steering. You might have a bent wheel. You might have lost a balance weight from the driveshaft. You need to have this looked at.