When you are viewing the list of private messages you'll see a check mark box to the right of each. Just select the ones you want, or check the box in the title bar to select all. In the dark grey bar at the bottom of the list you'll see Selected Messages with menu style button next to it. Choose delete from the menu, then hit the Go button to the right.
You can also delete your own messages in forums, if that forum allows editing. You choose to edit the message, then choose delete form the button at the bottom. You'll get a couple of radio buttons, one says Delete Message. Choose this and then click on the delete button below one more time. I guess they really want to be sure you mean it.
As a courtesy I never delete a message unless I do it almost immediately. Instead I'll just edit the content and explain why it is no longer relevant or what mistake I made. That way no one gets hung out to dry if they quoted or responded to it.
If you are using the iPad Forum app, you can delete a private message by viewing the message list, and swiping to the left across each one. A red Delete button will appear. Tap anywhere but the button to dismiss it without deleting.
If there is a way to delete your own forum messages in the iPad Forum app, I'm not able to find it.