An old chevy with a new shimmy

Just took my 77 chevy c-10 (250ci./th350) on a three hour round trip this last weekend (40-65mph). On the way back, I noticed a slight vibration in the rear which only occurs at certains speed. The vibration has gotten worse, so today I cycled the rear tires to the front and vice-versa, hopeing it was just a tire iusse. The vibration is still in the rear somehwere and only happens at 30-35mph, 40-45mph, and 50-55mph. Also, when I got home from the trip, there was a small amount smoke that smelled like burning tranny fluid, i checked the level and it’s still full. Any advice would be appericated.

Have you checked the rear differential fluid?

Tester