It does not pull to either side. Axles were just replaced and wheel bearings are checking out fine.
The car has a manual transmission.
I wondered about sticking non-Honda axles in it. It almost seems as if they could be a little longer and it would be better. I took it to a local front-end service shop today to have it looked at. After the guy drove it he thought it was a slight miss in the engine. I am not 100% convinced of that yet, but it is a possibility. We put the car up in the air to check everything out. I did notice that with the suspension unloaded and extended to max, the new axles that I just put in seemed to be "stretched out" at the inner boot. It is almost like the axles are an inch or so too short. As for the engine and transmission mounts, they checked out fine as well. However, the rear engine mount is not exactly easy to see or get to.
After driving it a little bit today to go to the shop I noticed that the shaking at cruising speed seems to be gone (finished the axle swap last night). Now the vibration seems to be more when taking off, moderate throttle, lower speeds, and is most obvious in 2nd gear.