Go to your Mail Preferences, then Accounts.
Choose an account from the list, and click the Advanced tab.
Uncheck the box "Enable this account", which will disable that account.
Do that for each account, until the Unread Mail indicator goes away.
That will be the account with unread mail.
Reenable that account, and disable all others.
That should make it simple to discover where those 'unread' messages could be - or that the 'messages' are some bogus left-over from Eudora, like a feature that Mail might not support. I don't know how to help you with that part.