Corp I and Corp II are a brother-sister controlled group as a result of ownership by individuals A,B,C,D, and E.

Corp II and Corp III are a brother-sister controlled group as a result of ownership by individuals C,D and E.

Are the above 3 Corps a controlled group?

I think you need some more facts. Have you read the Q&A's here on controlled groups?
http://employerbook.hypermart.net/QATopic.html#C6

The question of Affiliated Service Group will also come up.