We checked your PM statistics (we can see how many messages you have in your folders, but can't read the messages themselves), and the majority of your messages are in your Sent folder.
To go through them to delete, select the Sent messages folder from the drop-down menu in the "Folder Controls" section that appears above your messages when you're visiting you PM inbox. Select "Sent Items" from the drop-down and manage those messages just like you do those in your inbox.
The system saves a copy of your sent messages in this folder by default, so if you don't want to save a copy of a message in the future, you can uncheck the "save a copy of this message in your Sent Items folder" box that appears below the message composition box.
If you have any trouble, please let me know!