Are you trying to delete a message that you posted or someone else's
message that you downloaded?

You can cancel a news post (have it removed from the news servers) that
you made
OE5+: Message, Cancel Message
but many servers, including msnews.microsoft.com, will not honor the
cancel request (they are too easy to fake).

There is a roundabout way to delete a downloaded news post in OE5/OE6.0.
Do a Find for the message while the Folder List is enabled.  Left drag
the message from the results window to Deleted Items.  With OE 6 with
SP1+ you can use the DEL key to delete a post.

You can stop messages that you read from displaying in the list by
choosing:
 OE5+: View, Current View, Hide Read Messages.
And you can use filters to hide messages meeting certain criteria.

OE will automatically delete downloaded news messages when the news
server does.