83 Mercedes 300SD Rear End Problem

Hello everybody, my names Daniel and i just recently got this car about 1 month ago from a used dealership. My problem is that when i press on the accelerator either a 1/4 or more down i get a horrible vibartion coming from my rear when the car is going between 15mph and 25mph, you can feel it even more with the more you press on the gas. It sounds like a thumping, rumbleing sound that might be coming from the back tires. But after i pick up speed it stops making the horrible sound. And also when you light press on the gas and slowing picking up speed you cant hear the sound. I just got the car not that long ago and gave it an oil change (2 times cuz the oil was so damn black, i guess that happens to diesels. Anyways i might have pushed the car to hard by pressing the gas to much and even starting it in 2nd gear and punching it (I wanted to hear that turbocharger roar) I think thats where i went wrong, now im getting that noise, and worrying that it might by my tranny, or something in my rear end. Can someone plz help me find out what my problem is, I dont think that it might be major cuz i added more AT fluid and the Gunk* bottle to clean the AT fluid etc. And its not that loud anymore (i think). I dont know about the previous matience but the engine sounds fine (but it sounds like it needs a timing adjustment but I might be wrong, it revs at 33-3500 at 80mph.

Can somebody plz help me out?

Something has broken loose that holds part of the drive line in place. Check the engine and transmission mounts and the rear suspension mounts. The engine, trans and rear wheels put the most stress on their mounts in first gear at heavy throttle. Something that rotates is rubbing on something else.
Check the rear drive axles and CV joints as well.