How to find what packages do not come from a repository?

aptitude can do this query for you, with the ~o ("o" for "obsolete") search:

aptitude search ~o

this lists the packages that can no longer be downloaded.

I don't think there's an apt-cache search equivalent, and I'm not sure about synaptic.

For more info on search terms with aptitude, check out the section on search terms in the aptitude reference guide.

Run Synaptic. In the lower left series of buttons, select "Status". The list above these buttons may have an entry "Installed (local or obsolete)". When selected, this will show you all packages that were either installed locally (eg. from a downloaded deb file) or were installed via a repository but aren't listed any more. (There's no real way for Synaptic to tell the difference, hence they're grouped together.)

If you don't have any local or obsolete packages, this entry will not be present, so don't worry :)