There are a number of video editors around, some are free or low-cost.
Black Magic Design Da Vinci Resolve Lite is free. Sony Vegas is 50 $ or so.
Another low cost solution is Reaper. Version 5 (to be released soon) is 60$ and there’s a free 30 days evaluation that is fully functional.
Between these choices, and if you’re on Windows, Vegas has the lower learning curve. If you are really serious about video editing, Da Vinci Resolve is the one to go for. If you do mostly audio editing with video, Reaper is the obvious choice.
I’m not sure any of those work directly with AVI containers. Professional video works with a just couple of codecs (prores, H264…) and none of those get wrapped in AVI containers. But you can import/export most formats and a converter should be easy enough to find.
As your question is about video editing, you would do much better to ask on a video editing forum.
This is the Audacity forum and we can help you with issues to do with editing audio with Audacity.