I sure hope those downloaded avi files are legally obtained, or not copyrighted or whatsoever.
Anyhow, only MPEG video (MPEG2) can be burned on DVD-Video discs. Nero should be able to convert this AVI video's to MPEG, as soon as you start burning.
But... AVI is not a real format, AVI is a so-called format-container. There can be dozens of video types in an AVI file; maybe you are trying to put AVI files that are encoded with a little more exotic codec, like 3ivx or so, on disc.
I'd suggest to update Nero to the latest version (www.ahead.de). If that doesn't help, you'll probably need some other software to convert the file to MPEG.