Ok, I have a 97 Honda Accord with 143,000 miles. I've owned it for 900 miles; I resurrected it. The car runs good, and the transaxle doesn't slip but does act strange. The trans does shift hard between 1-2 and 3-4, I am in the middle of troubleshooting this, it may be the throttle cable needing adjustment and being to short, I'll check.

Here is my main issue, when I am in PARK and go to D4 or D3, the trans will go into gear within a second (as expected) and start to move the car forward, in the next 2 seconds you can feel what feels like the torque converter engaging or something, basically feels like it's gone into gear again, even though it's already in gear.

So you can be parked, foot on the break, pull the shifter into D4 or D3 and feel the trans go into gear, then 2 seconds later feel it again, as if it shifted again. This may be the torque converter I'm feeling the second time. If your foot is off the break and you shift the car it's starts moving then on the second feeling of "going into gear" 2 seconds later the car will start moving slightly faster. I am saying it may be the torque converter because when you drop it in R,1 or 2, this double engagement sequence doesn't occur, just one shift into gear and that's it. Fluid is a nice read looks fairly new, don't know what kind it is or how old. I will be draining it soon.

Final clue and I can't be 100% sure if this occurs but I want to bring it up. When I'm doing a good click, around 60 or so and completely take my foot off the gas suddenly I think I can feel a reverse of what I previously explained, the car will be coasting on the engine and 1-2 seconds after letting off the gas I can feel what feel like the torque converter disengaging.

Thanks for your help. Any ideas, knowledge or spit balling would be appreciated...

 

Check your mounts.
If they are worn, the transmission and drivetrain will clunk.
What happens is when placing an automatic into gear it first loads the gears in the transmission and differential. This is the first pull you feel. The second pull is when the drivetrain now loads against the mounts. With an MT you often don't feel this clunking as the initial release of the clutch is gradual.

The first movement can be exacerbated if you have pulled into a parking stall, and then have to reverse out. The clearances in the drivetrain are now at maximum when going from Drive to Reverse or Reverse to Drive. Since the gears were loaded for going one direction, and now have to go the opposite the gears in the final drive, differential, and any clearances in the axles will have to be taken up before loading the drivetrain against the mounts.

The D to R or R to D clearances can be removed when pulling directly into parking spot by placing the car in Neutral and let the car roll in the last foot to allow the gears to preload the opposite way. This will remove any clearance when you go to pull out of your parking spot.