Hi -
First - I would use ADUC on the Unity server - Active Directory Users and Computers to redirect messages sent to the EAdmin account to yours or another inbox that can be monitored. They are most likely, as you've indicated, messages sent to Unaddressed - users left messages at Opening Greeting or reached Opening Greeting because a subscriber was no longer associated with the phone extension. If you are a voicemail only site, you can use Message Store Manager utility - http://www.ciscounitytools.com/App_MSM.htm
and delete messages from user inboxes. You also have Exchange System Manager running on the Unity server, from which you can remove messages, although I'd make sure you have good backups before you do this. If you are a unified messaging implementation, from an administrator account that has full mailbox rights to the EAdmin account, you can add the mailbox to your Outlook view and clean up the messages that way.
Ginger