If Outlook is properly set up to check your email using POP protocol, you should typically not run into the over-quota problem unless mail is not being deleted from the server. Typically, your mail is stored on your local computer and not on the server, which would mean that you can only access it from the one computer where it is set-up.
If your account is set up as POP, and you are still running into problems with email quota it means that you don’t have Outlook (or other mail program) set to delete mail from server – a copy of all your messages remain on the server even if you deleted them from your local computer’s Inbox. To change this
1. Choose Tools–>Email Accounts and click on “View or Change Existing Accounts” to select your account.
2. Select Change….
This opens the email accounts window. Note that Internet E-Mail Settings are indicated as POP3, which tells you that your account is set-up to use POP protocol.
3. Click on the More Settings button in the lower right. In the new window that appears, select the Advanced tab and look for Leave a copy of messages on the server. You can click to uncheck the box if it is checked or you could check it to leave a copy in the server, but the latter means that you should specify to remove messages from the server after a small number of days, no more than 7.
Note: If you really must use POP and you must access your email from numerous other computer then check “Leave a copy of messages on server.” then, check “Remove from server when deleted from ‘Deleted Items’.” That way, when you delete a message, it will also deleted from the server rather than being left there to clog your account.