I would guess you should be okay with a piece of oak as a divider. I've always been under the assumption that spanish cedar is used to line humidors because of its ability to maintain a more constant humidity, so I don't think a single piece of oak is going to cause any harm.

As far as storing different cigars together, the only hard and fast rule is to NOT store "flavored," or "infused," or "aromatic" cigars with regular cigars. Some people like to store their corojos with their corojos and their maduros with their maduros, but I feel that if the tobacco has already fermented and cured in a barn in the DR (or wherever), the marriage of flavors is going to be minimal, if that.