Podcasts have the same syncing options as the Movie and TV show screens. You can choose to sync none or all of your podcasts, as well as those fitting certain criteria. If you wish to sync some podcasts, but not others, choose "selected podcasts" and then click the ones you prefer.
The next tab, iTunes U, lets you sync educational content downloaded from iTunes to your phone. The interface for syncing iTunes U content is the same as for TV Shows and podcasts.