Sending, receiving, and organizing email in Outlook.com
Thanks!
Does the issue occur in Outlook Mobile?
Deleting emails doesn't free up much space, as they take up very little room—except for emails with large attachments.
You can delete files from your OneDrive that you no longer use. Be careful, though, as these files might be synced with your computer (folders like Desktop, Documents, and Pictures are usually synced, so only delete them if they are truly unnecessary).
You should also empty the Recycle Bin, as it counts toward your storage usage.