Those are too contrived.
You could, I guess, make Owin or Owen out of Oliver Edwin, but if you were going to do that, why not just name him Owen and be done with it?
Personally I like Eddie as a nn much better than Ollie or Oliver or Edwin. I like Ted too.
Before you criticize a man, walk a mile in his shoes. That way, when you criticize him, you're a mile away and you have his shoes!
Steve Martin