Hmmmm... I'm honestly not sure what's going on here; you should be able to just click the shape and drag into your document.
Assuming this doesn't magically start working, the best thing to do is going to be to use "Send Feedback..." under the help menu to send the support ninjas an email - that tells them exactly what version of OmniGraffle you're using and gives them some other information which helps them help you.
One thing which may help would be for you to include some screenshots of what you are seeing when you try to drag shapes from the stencil
(You can take a screenshot by pressing command-shift-4, which will give you a selection cursor. Tap your Space key, click on the window you want to capture, and when you release the mouse the image will be saved to your desktop as 'Picture 1', 'Picture 2', etc.)
You can then drag the images to an email message and send them to us. We'll use the information they contain to try and figure out what's going on here...