I have tried Xcode, Vidconverter, Handbrake, but none of them deal with a blocky avi except to make it bigger resolution. Is there any software that can actually define the video better?
If it's blocky, there may be dropped frames. You might try TSmuxer. Can you upload one to something like dropbox and provide a link for it here?
If you're getting blocking then your bitrate settings are prpbably too low. The quality of the source is also important. I've ripped and transcoded entire series using Handbrake with quality that is almost visually indistinguishable from the original. All my transcodes were done to Mp4 container for universality.
Your converting avi that's your issue right there. To transcode you need a large mother file that as my nemesis above states (aka Sophocles) has a high bitrate then recode from said mother file (if possible trim front & end credits to remove junk you don't need which will help improve the recode quality wise). So find larger files you can re-code or download ones that have already been done
It's always best, in these situations, to have something for us to work with so we can offer the best advice. Asked for a sample file but it doesn't look we're going to get one.