First of all, I found out that Prof. Oak is Gary's Grandpa. If there was any connection between Ash and Prof. Oak, it would be that Ash is his half-grandnephew/ or real grandnephew. Second, Giovanni's relation with Ash is very slim to none. Giovanni's son has red hair, and hasn't shown up in the series, only in the Metal version games. If Ash is Giovanni's son, Red-head would have to have a separate mother.
That's what I thnk about Ash's father being a real person from the series. Though I'm still curious, so I made up a semi-logical fiction story about him(I'm posting this to all forums who wonder about Ash's dad, and see how they think):
One of the days that Ash's dad went on his journey, Giovanni found him and asked him to do pkmn genetic research. He accepted, and was one of the few to find Mew's DNA. Once he helped find the hair, Giovanni betrayed him.
His body vessel was used as Mewtwo's structure (which would explain Mewtwo's human-ish body) and got his mind erased from the opperation.
That's what I think. I don't care if you disagree, it's just my crazy idea.