I'm looking for an example or official documentation showing how to include a third party library as part of a Tropo hosted Javascript application for handling calls.
You really won't find one. However, it appears that Tropo is using the JVM's scripting engine, which (for JavaScript) is based on Rhino. I'd expect you can just upload your third party library and then use Rhino's load function to import it. You'll need to make sure your third party library doesn't depend on any global variables that don't exist (such as window,document, or pretty much any of the browser-specific objects that are out there) but that should work for you.