It sounds as though you're trying to delete them from an IMAP folder...

Q: How do I get rid of deleted messages from my IMAP folders?

A: When you delete an email from your IMAP mail folders using Outlook, it still displays it but puts a line through it. These items are not deleted permanently until you purge your deleted messages and therefore still use up file space. Note: It is not possible to set Outlook to automatically purge your deleted messages.

To permanently remove (purge) your deleted emails, choose Edit | Purge Deleted Messages.
To add the Purge Deleted Messages button to your Outlook toolbar:

Choose View | Toolbars > Customize
Choose the Commands tab and click on the Edit Category.
Scroll down the commands list and select Purge Deleted Messages.
Click and drag the Purge Deleted Messages button to the toolbar at the top of the screen and drop it next to the Delete button.