Did you inspect the axle before putting it in? If not you're gonna have to take it back out and take a look at the axle spline to make sure the C clip is there and that there is no damage. Take pics with your phone and upload to photobucket and post them here if you find something weird looking.
Make sure you have the right seals in there. Mine kept popping out when i swapped a civic si tranny in cause it still had the civic si seals.
This info right here is incorrect, oem part numbers for both b16 transmissions and acura integra ls/rs/gs transmissions (probably even gsr and type r but I didn't check for those) are the same. If you went and got an tranny oil seal from pepboys/oreilys/autozone/napa please make sure the part number is the correct oem replacement and no thicker or different.
First AutoZone axles=cheap crap. Are you sure you're getting them in all the way and the C clip is in good shape? If it is knocking and makng noise then I bet that the axle isn't in all the way because it would make noise if it is longer than it should be indicating that it isn't fully in the tranny. Hold the axle straight and take a big rubber mallet and hit it until you her the click. A new axle especially is difficult to put in by pushing it with your hand.
Check the Thunder Grey Teg 1988 Toyota Tercel (1500cc of pure muscle!) Traded in for a.... 1994 Integra LS (Currently has a 1999 JDM ITR engine and tranny) Sold to buy a.... 2005 Acura TL Navi 6 Speed Manual