If I've read ScottP's reply, above, correctly.... you should join L2 to R1; then measure the voltage from L1 to R2. This should be 240v or thereabouts.
Before you do that; just to confirm, your 120v readings are L1->L2 and R1->R2, is that correct? If L2->R2, then something fishy is going on...
Without being able to see details of your switch/socket wiring, I don't think we can diagnose further: Can you take some photos of the switch (front & back), and maybe a diagram showing how you've wired it together, and attach them to a reply (use the "Attachments and other options" link, below the message edit box, when you make a reply. Also, please reduce the size of any photos to something sensible: 800x600 or 1024x768 or similar, thanks.)