It's been a long time since I've used Overdrive for anything besides getting eBooks brom the library. As I recall it might have been one of those apps where you could transfer files to and from the app's reserved storage area when you attached it to a PC and opened iTunes. You'd highlight the app, and you'd see an area of the window in iTunes with the files you could select and transfer to your computer.
I don't think I'm going to be much more help, but here's an Overdrive help page you can browse:
For iTunes purchases:
Since you did not specify the app, yo may be able to use File Sharing in iTunes to get them from the app to the computer.
Otherwise a third-party program like PhoneView or TouchCopy or iFunBox may work but I do not know since I do not know the app you are using.
I failed to mention that I am using Overdrive.
I have tried searching for the files on my iPod and cannot seem to find any of them.
I did to a Transfer Purchases and a Backup from within iTunes, but I cannot find the back up or the audiobooks when I can find pictures and documents.
I guess I am not sure where to look. I just assumed that you could teansfer between ODM apps.
Overdrive media are not iTunes purchases so they do not transfer with:
Overdive media are copy protected so you can only read them via Overdrive. I do not understand what you mean by free books and are now paid. Overdrive are typically books for a public library.
You can try looking on your iPod via a third-party program like PhoneView, Touch copy or the free program iFunBox