So I had the vibration coming from my car as well and I would like to share my experience.
This thread helped me a lot as there were some posts that helped me pin pointed my issues and some member's description helped me to reassure that my issue was an axle issue and not an engine mount issue.
My car felt as if the engine was shimmying side to side while accelerating right under 3000RPM and at WOT all the way to redline. At first I thought it was the engine mounts, but since my car idles smoothly, it was hard to blame the mounts. I then thought it might have been a bad tune so I went for a datalog and everything looked smooth. My vibration didn't travel through the steering wheel. So the steering wheel wasn't shaking during the vibration. Although the whole car seemed to be shaking.
I then did what a member suggested in order to check the axles. Went under the car, held onto the inner joint and outer joint, then twist them in opposite directions. The passenger axle was pretty solid with very little play. But the driver side axle had significantly more play and made a clanking/metal on metal noise every time I twist. So I switched out the driver side axle (OEM at $500

) and the vibration immediately went away. Then my OCD kicked in and I decided to change out the passenger with OEM axle as well.
If you have a manual transmission, remember that the driver side axle is not interchangeable with the automatic transmission one. Passenger side axle is interchangeable. Info on part number for different transmission can be found here:
http://www.tsxclub.com/forums/1st-gen-problems-fixes/46304-axle-difference.html#post678532
In summary, if you're having vibration under acceleration or under load, especially going up hill, then more than likely it's an axle issue.