I don't have an ipod so I don't know anything about them but it looks like you purchased the audiobooks from the istore. How could your local library have your credit card details?
I wouldn't have thought that you need an itunes account to use Overdrive.
The only thing I can see in the Overdrive instructions is the bit about setting your ipod to manually manage music. See below.
What requirements are there for transferring OverDrive MP3 Audiobooks to Apple devices? •OverDrive Media Console v220.127.116.11 (or newer) for Windows or OverDrive Media Console for Mac v1.0 (or newer). •iTunes v9.1 (or newer) for Windows or iTunes v18.104.22.168 (or newer) for Mac. •On Mac, iTunes v9.1 (or newer) is required for transferring to the iPad. iTunes v22.214.171.124 (or newer) is required for transferring to the iPod shuffle. •The device must be formatted for use with your operating system. •The device must be set to 'Manually Manage Music…'
How do I set my Apple device to 'Manually Manage Music…'? 1.Connect your device to your computer. 2.Open iTunes. 3.Locate the device in the left navigation panel (under heading 'DEVICES'), and click the device. The 'Summary' screen is displayed. 4.Place a checkmark next to 'Manually manage music…'. 5.Click 'Apply'. The iTunes 'Summary' screen refreshes, and your changes are saved.