You should expect the avi files to expand in size considerably when you convert to DVD-video. The amount of bitrate necessary to maintain high quality is fairly high in the mpeg2 found in DVD-video.
So you should plan to divide the episodes by length of time. Don't try to put more than two to two and a half hours of video on a single layer DVD.
You can use a free program called AVStoDVD to convert your files with a menu so you can select each episode. There is a link to a guide to the program down below, in my signature.