yes, but unless your dvd player is proper bo, it wont have the right codec to play the avi's on, as most of them tend to need a xvid codec.
whilst you're right, there's software out there, i'm yet to find something which does it all, without needing the user to posess a phd in piracy...you need to work out your frame rates, your res, your ratios, bitrates, etc. for conversion to mpeg2, and it's often difficult cos the sources will be different and not all encoded in the same way. and i'm guessing your lost episodes will be in ntsc, which might need sorting out etc.
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