1. You can go to your inbox or sent folder of PM's. When the list appears, select the checkbox at the top and to the right of the number of messages. This will select every message on the page. (the checkbox would be to the right of the #1634 in my pic below)
2. Now scroll down to the bottom of the message list at the bottom right, and select the dropdown arrow box of "selected messages" for a list of options for things to do with your selected messages. It's default is "move to folder", but after you click on the arrow, you have more options including delete.
If you just want to delete them, then select delete. After selecting delete, then click on the GO button to the right of it.
You will need to do both for your inbox and sent box if you want both deleted.