Nobody can tell you anything without proper system info or other technical details like version of AE, audio configuration, files used and so on. Aside from audio hardware realtime mixing issues this could also be different volume levels in the files. In any case, AE is probably the worst tool for any such work, so if possible, render out your video and add the sound effects in Premiere or Audition.
If you want to do a good audio mix then you need to either mix the audio in Audition (it can work with movies) or Premiere Pro. You should be creating shots or short sequences in AE, Editing the shots in Premiere Pro, and finalizing the audio mix in AE.
You can do some very basic audio mixing in AE using the Audio effects included with AE but they are really only usable for the most basic mixing tasks. To learn how to use them you can search for some tutorials on Mixing Audio in AE or just poke around and see what you get. Be warned though that there are some bugs in the Audio Effects that may bite you on rendering.