I'm switching a lot between OS 9 and OS X (Classic is too slow sometimes). In OS X, I check my mail with Eudora beta for OS X.
Because it is a Carbon app, you can use it under OS 9 with CarbonLib, but then you don't get your mailboxes, prefs etc. You can solve that by making an alias of your Eudora Folder from your OS X user directory (not the Eudora Application Folder) in OS9Drive:Documents.
Mac OS X Hints
http://hints.macworld.com/article.php?story=20020222092050753