I know how to delete videos;just hold my finger by the side until the delete option comes up. But I don't know how to delete audio and video podcasts that I don't want without connecting to itunes on my pc
It happens to me, also. It appears to be a serious bug. I even set the iphone to airplane mode to be sure they didn't reappear somehow over the air. They are kept somehow in memory. I fixed it by setting the podcast preferences in iTunes to keep only the 3 most recent podcasts, and the old ones disappeared permanently from the phone. Forces you to keep up your listening, too.
Well, that worked for a while. The real way to delete a persistent podcast is to go to Podcasts in your iTunes library, select view as list from the toolbar, and completely delete (control-click on a Mac) the podcast episodes you never want to hear again. Don't know what auto delete verus don't auto delete does as a choice. That doesn't appear to work.