Go into iTunes and check how you've got your podcasts set up to sync. Plug in the iPad, select it in iTunes, and go to the podcast page.
If you've got it set to automatically sync the newest or oldest, it's going to to that every time. If you've got it set to sync unplayed and you delete the podcast from the iPad before syncing again, it has no way to know it was played, so it will add it again.
So, either select one of the unplayed options, and let the iPad remove it during the next sync, or unselect the Automatically include box and select the podcasts you want manually, by checking the box next to them.
When you delete podcasts that you sync manually they will stay in iTunes, but uncheck themselves and no longer sync to the iPad, unless you change the settings again.
Deleting stuff from the iPad does not delete it from iTunes. If your sync profiles are set up for some kind of automatic selection things may get added back after the next sync, depending on exactly how it is set. When you really want something gone for good, you have to delete it using iTunes.
While that may seem like a bug, or annoyance at times, it's also a safety feature. It means that deleting things from you iPad just to free up some space doesn't mean you have to worry about losing a valuable file forever. To do that you've got to mess up on the computer, where hopefully you've been doing your backups