I am doing a research on ranking the different oil groups in the area of resistance to varnish formation. I would like to rank them in this regard. I would also like to see if synthatic oil has more resistance to varnish over the other groups.

Depends on what you mean by varnish - impurities or basestock resistance to oxidation. Also solvency comes into play to keep initial products dissolved. So basically if talking S,N impurities Varnish resistance would be 3>2>1. Basestock 3>2>1. Solvency to keep small amount of oxidation products soluble 1>2>3. But once antioxidants deplete, especially phenol type antioxidants, varnish will occur regardless of the basestock especially for group 3. There was a paper at latest NORIA conference in Columbus May 2006 by Wooton (I believe) that talks about varnish process, what products are, etc. Also ASTM had symposium last December also on oxidation problems/varnish of turbine oils-check website to see if available