Podcasts that I've unsubscribed from and deleted keep coming back

There are about five podcasts that I am trying to unsubscribe from, and iTunes won't let me. I go to Podcasts in my iTunes, right-click to unsubscribe from them, and then right-click to delete all the podcasts, and it looks like it works. But then next time I go to my iTunes, they are back like they were—resubscribed and downloaded. It seems to happen if I connect my iPod nano, iPhone, or iPad to my computer and then it's a syncing error, but I would think that iTunes on my Mac would be where I can control all of my podcasts. I have it set on my phone so that podcasts do not sync and don't download at all, and obviously my nano's content is only controlled by my iTunes, and then I've tried to manually sync with my iPad but honestly I don't really sync my iPad anyway. I've tried to go to Download Episodes --> Off in the podcast settings before I unsubscribe and delete them, but that doesn't seem to work. Any help would be much appreciated, as this pretty much is driving me insane. I've unsubscribed and deleted them three times already today.