My 96 Accord shakes when I put the car in 3rd and 4th gear only. I had gotten my wheel bearings replaced twice already and they seem to have fixed the prior vibrations, but this problem had just started happening. I've realized that when I turn the car slightly to the right while it's shaking it stops but continues when I put the wheel straight, or when I put it in 5th gear (I don't know why). Anyone have a clue what the problem can be? I have the feeling it's the tie rods causing it, but I'd like some input from someone else. Thanks!

 

Inner outer tierods, ball joints, wheels unbalanced/rims bent, sway bar links worn or broke. Could be numorous things

 

I have a similar problem to what you are describing. Hope you find a resolution to your problem!