Like Alia, I haven't heard of Shiva oil sticks, but from your blog post, I am intrigued. I am pretty sure that Sculpey clay softener is made of mineral oil, but I can see that if you get too much on the surface, it would cause cracks. I have read about people using a dab of Vaseline to smooth the surface of their beads before curing them. I don't think that oil products in and of themselves will damage your polymer clay pieces.
I was going to suggest scanning Glass Attic (
http://glassattic.com/), but I see you're already familiar with that site full of nuggets of knowledge!
I checked a couple of my reference books. The Polymer Clay Techniques Book says that you should not use enamel paint on clay because it will never dry completely. However, the fact that you've got sticks makes me think they are more like oil pastels.
I think Alia has a good point - experiment and see what you think. You can always apply a glaze if you need to protect the finish.
Keep us posted!