Shaking and vibration

I have a 2001 Dodge Ram 2500 5.9 gas engine
Laramie SLT.  185,000 on the odometer.

When I start down the road there is mild shaking.
When I let off the gas, there is a short but loud
vibration ( like driving over the rumble strip on the
highway ). It also does this briefly when getting
back on the gas peddle. At different speeds the
shaking becomes more intense and is worse when
going up and down hills. It just had a tuneup, oil
change, fluid checks, new tires mounted and
balanced ( lugs have been checked and are tight ),
and a new radiator. Prior to this work the truck has
been sitting for almost 4 years. My brother hit a
deer and parked it because it ruptured the radiator.