I have an iPhone 4 (A1349), updated to iOS 7.1.2. I synch on a McBook Pro.
My issue is that I have unchecked synch podcasts in iTunes, and yet podcasts are still listed on the phone's Podcasts app. I have tried both to uncheck Sync Podcasts in iTunes and to keep it checked but to uncheck the Automatically include ... box. In both cases the podcast app still lists the podcasts I subscribe to, and some episodes under those folders. The episodes listed include cloud as well as downloaded episodes. The episodes are playable. An example of such a podcast is Freakonomics Radio, but all my subscriptions are listed.
Best Answer
Turning off the sync options will stop your phone syncing new episodes, but it won't remove the episodes that have already synced.
If there are episodes on your iPhone that you want to remove just drag the entry for the episode to the right to reveal a Delete button. Tap the Delete button and it will remove the episode from your phone.