Many of the Oddenino ancestors that settled in colonial Virginia were from Germany, specifically the Palatinate area of western Germany. More information on this area can be found at this link:
From the above link:
The Palatinate extends from the Rhine plains to the Vosges mountains in France. The velvety hills of the Palatinate Forest function as a temperature and weather buffer. Hence the area is a sun-drenched region whose mild, almost Mediterranean, climate supports the cultivation of kiwi fruit, lemons, almonds and figs alongside the grapes. Millions of vines grow along the German Wine Road which begins in Bockenheim and runs 80km south to the German Wine Gate in Schweigen on the French border. The Palatinate offers beauty for all senses to enjoy.
Thanks to the gracious permission of the publisher, here is an illuminating article on the Palatinate from Family Chronicle Magazine found in the July - August 2004 issue by James M. Beidler titled What's a Palatine, Anyway?
Here is a link to a website for Palatines to America for more information on researching German ancestry from the Palatinate.