Managing personal Outlook.com account settings, security, and privacy
When you log into http://www.outlook.com/, do you see "Outlook.com" or "Outlook Mail" (or "Outlook Email") at the left end of the menu bar?
If you see "Outlook.com", click the Options gear, then "Manage rules". Click New. The default condition will be "Sender contains". Put your own address to the text box top the right of the condition. Click the plus sign beneath the "Sender contains" condition. The default new condition will be "Recipient contains". Enter your address in the text box to the right of that. The default action will be "Delete". Click "Create rule".
If you see "Outlook Mail" (or "Outlook Email"), click the Options gear. In the left had column of options, click "Inbox and sweep rules". Click the plus sign in the "Inbox rules" section. Give the rule a name. In the "When the message arrives..." section, click the "Select one" condition drop-down and choose "It was sent or received", then "Received from". Enter your own address. Click OK. Click "Add condition", then "Sent or received from", then "Sent to". Add your own address. Click OK. In the "Do all of the following" drop-down, choose "Move, copy, or delete", then "Delete the message". Finally, click OK at the top.
Remember, though, that these are Inbox rules. They won't operate on any message delivered to the Junk (for Outlook.com) or Junk E-mail (for Outlook Mail) folder.