Although not a fully supported feature, here is how you can transfer episodes between podcasts (or even bring over external episodes into Jellypod).
Step-by-step Guide:
Visit the originating Podcast (where the Episode will be transferring from).
Click the ... menu on the Episode's row
Click "Download Audio"
Visit the destination Podcast (where the Episode will be transferred to)
Next to "Edit Podcast" click the ellipsis (..) button in the top right corner
Upload the MP3 and add a title and description.
Click Done.
Note:
If you're transferring from somewhere external, download the MP3 file and start from step 4.