I have a book which was published in 1987 for the 700 year anniversary of the little German town of Adelshofen(Eppingen) in Baden-Wuertemburg, not too far from Stuttgart . In it is a list of emigrants to North America. A Johann Andreas Illig emigrated in 1727 with one other person, and a Johann Rudolf Illig emigrated with 3 others in 1732.(See Illig message board)
The book mentioned somewhere that the named changed into Illg. There is a list of farmers, after WWII, and an Edwin Illg, Hilsbacher Str. 6, is mentioned.
There is also a picture of German WWI vets of Adelshofen, and a Karl Illg is among them, a Georg Illg of Adelshofen died while serving during WWI.
In case your ancestors came from the Adelshofen area you might be interested in this little book. It is printed in the German language