How does one animate objects in VIZ so as to end up with a transparent background in the .avi file which ultimately will be layered with other .avi files using video editing software?

What video editing program are you going to use?
If you are going to use Sony vegas you can make the background Black
and then choose the property “Add” on that video layer, making the background transparent

Or you can use the effect Chroma keyer.
Select a backround color that is unique, that none of the other objects have.
then add the chorma keyer, and select the same color as the background, and the
background will also become transparent.

GL

Or save a Targa sequence instead of an AVI file.  Make sure to save the alpha channel with the Targa.  Saving to a sequence of still images is preferred over avi, anyway.

3DS Max Design 2011 64-bit - Advantage Pack
Dell Precision T5500, Dual Six Core Xeon X5650 @ 2.67GHz, nVidia Quadro 5000, 24 GB RAM, Win 7 Enterprise 64-bit
Minneapolis, MN, USA