If your emails in Outlook are gray out and strike-through, but won't go away, do a purge.
I couldn't figure out how to get rid of these entries for a very long time:
On a recent googling, I finally learned that I need to do a purge to get rid of it. I use IMAP to access my emails, and I suppose Outlook is cautious about deleting things. In Outlook 2007, the PURGE option is located under the EDIT menu.