2 things
a lot of AVI subs come with subs that are auto loaded (do you see a file probably with an srt extension and the same name as the AVI, remove/rename this and the subs will vanish.
2) As for the black bars: if you have subs that are in the black edges of the avi then do that (or trim and add a border) if you have them in the picture then I suggest you mess with a logo remover, you will get a good bit of noise from there though (I am fairly sure you will have seen a logo removed TV show at some point, expect it to be as good (the options used are not alwasy the best) or slightly worse (a logo is less than 10% of the picture.
FFDshow (the app I wager is used to decode video on your system) has the option and there is a virtual dub filter from donald graft/neuron2's site (the one linked on virtual dubs homepage). I believe mplayer's encoding part also can do it although I tend not to use it so you will have to look it up. I also suggest even if you use the FFDshow option then you look up the vdub filter as the help file for this details all that you want to know.
Edit: if it is a .divx file (a slight tweak on the AVI container) then you may get lucky and have soft subs installed.