I have a V-Studio 100 setup.  I would like to work on my Sonar VS files without being connected to the V-Studio surface.  How do I assign the output to my computer's sound card and redirect the tracks to that output so I can hear it through headphones?

If your computer card supports it, you should be able to assign input and output just like you did with the VS-100 (you might have to switch it from ASIO to some other driver option, though)
 
However, performance with onboard cards will be mediocre at the best ... no one would seriously suggest using onboard cards, neither do I ... unless it's broken I'd stick to the VS-100. it's a really decent interface ...