Extremely shakie tires

I have a 1997 honda civic, and am having a very bad problem with my right rear tire. The car is normal until i go over 60 mph. Between 60 and 80 mph the car shakes very bad, From behind my car it looks as if the right rear tire is constantly going on and off the road, up and down. After 80 mph the car completely smooths out and drives normal again. I have replaced the struts and bought a whole new tire and rim...
Any ideas?

Did you get the tires balanced, and aligned?

try balancing the tires but also have your mechanic look at the trailing arm bushings .when they go bad you have similar conditions .post your findings

I have to ask the obvious question, were they mounted the right way?

Check shock, bushings, bolts. anything that may be loose.