You have some ways (only if you need to convert AVI to DVD, since DivX player support loading of subtitles):
1) permanently encode the subtitle in the video, whan you convert AVI --> DVD
2) convert SRT to SUP with SRT2SUP, and author video (M2V) + audio (AC3 or MP2) + subtitles (SUP) ---> DVD with IFOEdit.
If you do 1) you permanently encode the text over the pictures, and of you do 2) the subtitles are selectable (and you can put many languages).
Before working hard, chech the SRT subtitles are in sync with the AVI. I use BSPlayer.
There are two ways to fix synchronization:
1) if the un-sync is constant, SybTitle Creator or SubTool can shift the subtitle (SubTool command: synchronize)
2) if the un-sync is un-constant (and, therefore, the subtitle's and the movie's length are different, the SRT and the AVI have different framerate (23,976=NTSC and 25=PAL) and you need to change the framerate of the subtitle (lower to shorten it or larger to lenghten it, (SubTool command: change framerate)
Well, if you want to create an AVI (subtitled ot not), you need a codec. Remember that XviD is simple to use and free; DivX is a little more difficult to use and isn't even free.