First thing, you don't need all the codecs and packs that you installed. You can start to run into problems when you have more than one codec installed to read the same thing (or multiple versions of the same codec).
-I don't know which version of the amvapp you have installed, but it may have already come with ffdshow (one of the main components of CCCP).
-k-lite is bad, and should be uninstalled (it also contains ffdshow, along with about 3 copies of every other codec in its list)
-CCCP should be able to take care of the vast majority of files that you run into, including divx and xvid. It shouldn't hurt to leave divx and xvid installed though (might need to configure ffdshow if you run into problems, but we'll cross that bridge when/if you get there)
Now onto the video problem. Your .avi files are probably encoded with either divx or xvid.
You can get MediaInfo
which will tell you (among other things) what codec your file was encoded with. GSpot
should also work fine in this case (GSpot doesn't need to be installed like MediaInfo does, you just run the .exe)
Without going into too much detail, xvid and divx are bad for editing and usually will mess things up at some point. Using lossless codecs like huffyuv or lagarith is preferred for editing. Lossless = big files, so unless you have tons of patience and hard drive space you should probably not re-encode entire episodes with a lossless codec. Instead, you can open your files with virtualdub and select the parts of the episode that you want to use and only re-encode those parts.
queue the famous quote (virtualdub and virtualdub mod are pretty similar, but you should get virtualdub if you don't already have it)
open the video file in virtualdub mod go to video->compression->Huffyuv
then go to file->save
use those to mark the beginning and the end of the "clips" you want so you can save room