Are you trying to convert the avi and mpeg files into dvd compliant format? Or are you simply burning to a disk as data files and playing on a dvd player that can handle avi files by itself?
If you are converting there are many different choices. ConvertXtoDVD is a popular program on these forums, but is not free. FAVC is a free conversion program, and should produce better results than Nero Vision. You then burn the resulting dvd video onto a disk with ImgBurn.
The problems in the burn portion could be from many different causes. Do you have the log file from Nero? It should show what was going on.
Check to make sure dma is enabled for your drive. And tell us what burner, and what blank media you are using.