Do a search on this board for IMAP and deleted and purge. You'll discover that the way servers work, a message that's deleted ordinarily remains in the inbox but marked as deleted. Mail programs usually hide those messages that are deleted, and only move them to a separate folder if you configure the server to do that. On the iphone, you can do this at Settings>Mail>youraccount>Advanced, and selecting the folder that you want your deleteds to go to. If you use Mail on your mac, the folder to choose will be called "Deleted Messages", and in your webmail app, if you use one, you'll want to specify that messages that are deleted are moved to that folder. In Entourage, which I haven't used in a long time so I don't remember exactly where the setting is, you'll have to do the same thing.
Note that in Mail, the folder called Trash is just a generic name for whatever folder you happen to have set for deleted messages, which by default is "Deleted Messages" but you can actually use whatever you want. If you chose a different folder, the "Deleted Messages" folder would appear in your hierarchy as a regular folder, and the one you chose would now appear as Trash on your mac.
To get rid of those deleted messages that are in your inbox and crossed out, you'll have to issue the Purge command, which you'll find in one of the menus in Entourage. You can do that before you change the deleted folder to get rid of them first if you like.
