I have an old Swagman hitch rack that holds 4 bikes by clamping the top tubes. There is a V notch type slot in the platform for each bike. A plat with matching V notches bolts down on top of the platform to clamp all 4 top tubes simultaneously.

Some new bikes (notably from Specialized) do not have round top tubes. Are there any successful strategies for clamping these irregular shaped top tubes in a rack like mine?

Check into one of these:
http://www.deltacycle.com/product.php?g=31

Check into one of these:
http://www.deltacycle.com/product.php?g=31

I bought a similar item for my girlfriend's bike, which has a step-through frame. they help, but they aren't perfect. buy a cheap tub-o-bungees or tie-downs at a hardware store and see if strapping it creatively will work first. Those faux top tubes aren't terribly secure, you will be adding a few straps and bungees anyhow.