ASF is the same as Windows Media Video or WMV, it's microsoft streaming format. Anything after V4 is a closed format. For the past year or so we've been using WMV V7 and for about two months now it's V8. No matter if it's WMV or ASF it's the same thing. By closed format, it means that you cannot open it in an editor or conver it.
At this time, there is nothing (within common sense) that can convert WMV or ASF, however there is a rumor that the final version of Movie Maker for XP will be able to edit or convert these formats but it's not official by far.
As for AVI it depends if you have access to the AVI codec and if it's a free one, some codecs are read only and some are read/right and free like Divx.
for starters I would recommend
Sonic Foundry's Video Factory it's only $70US. It's able to 'read' most mpeg's and avi's and can then save them to other formats like divx or mpeg. It has the built-in Ligos mpeg encoder. It can save to QT or RM but it can't read those formats. Good luck.