You should be able to transfer them to iPhone using the desktop Overdrive Media Console, but they will show up in your Music app. If they were tagged as audiobooks, they would show up in that section of the Music player, but mostly the books I've downloaded have been tagged as Fiction, or Business, Children's, Fantasy etc. IIRC, the tracks of each "album" in the Music app will play in order by default, but it won't save your place if you listen to something else.
I recommend backing up the files in any case - sometime ago, Overdrive updated their iOS app, it wiped out people's libraries, and the free SYNC books could not be restored.
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