What device is this you are using Overdrive with?
Quite a few people have login/registration issues with Overdrive on tablets.
If on a tablet, try installing the Bluefire app and authorizing that with your Adobe ID.
You may find you can just use the Bluefire app.
You may find (no promises) that authorizing Bluefire makes Overdrive work, as the authorization is really for the device and not for the app.