How do I delete all Podcasts at once in iTunes
In iTunes, go to the Podcasts library (View > Media Kind > Podcasts) and view as Classic List (View > View As > Classic List).

Your list of podcasts should then appear in the main window. Select All (Edit > Select All). Click on the 'Unsubscribe' button in the bottom right corner.

This doesn't delete the files, it unsubscribes you so that you stop getting updates and new files. You can keep files even after you unsubscribe. To delete all the files, select all the podcasts you want to obliterate and type 'delete'.

NB If some of the podcasts are no longer subscribed to, the button will be 'Subscribe'. If you deselect those podcasts (Command-click on any selected podcast to deselect it) then the button should change to 'Unsubscribe'. If you start at the top and use the down arrow key, you can go through the list and see which podcasts this would apply to.