Marty,
If you click on the Private Message prompt below your screen name (top right) It will bring you into your message folder. Click on the top message count(it will say "private message in folder: inbox. Its the box directly to the right, click on that) and it will highlight all your messages. Then at the bottom of the screen it will say 'selected messages" with a drop down. Select "delete" then click the "go" button next to it and it will delete all selected messages. If you want to delete sent items too, there is also a drop down labeled "Jump To" it is located under your colored bar graph. Hope this helps