It depends on how you load your content. If you use automatic syncing, you cannot delete items from the iPod's content list in iTunes. For podcasts, you need to use the iPod's Podcasts tab in iTunes.
Select the iPod in the iTunes sidebar, under DEVICES. If the sidebar is hidden, from the menu bar, under View, select Show Sidebar.
To the right, there is a row of "tabs" (starting with Summary). Click on Podcasts there. This the the Podcasts tab, where you tell iTunes how to sync podcasts to the iPod.
If you are using automatic syncing already, Sync Podcast should be checked. Change your settings and selections below, to unselect from syncing the podcasts (or the podcast episiodes) you want to remove from the iPod. Then click Apply.
If you use the manual method (drag and drop items on iPod in iTunes) to load content, you should be able to remove podcasts from the iPod's content list in iTunes. In your description, where are you looking to select the podcast and press the Delete key.