If I control Gisela, Blade of Goldknight and I use something like Shining Shoal or Reflect Damage to redirect damage, will I do X damage, where X is halved coming in by Gisela and then doubled going back out, or can I stack things such that I avoid Gisela's halving ability and thus do 2X?
For example, I'm attacked for six damage. If I use a redirect ability, will it be halved to three, and then doubled to six when I point it at my opponent, or can I apply the redirect effect before Gisela halves the incoming damage, and so do twelve damage to my opponent?
Both the redirection and the doubling/halving of the damage are kinds of replacement effects. As such, the affected player, or the controller of the affected object chooses one to apply and applies it, and afterward chooses another to apply and applies that, and so on, until no more effects are applicable. Then the modified event happens.
So if damage would be dealt to you or a creature you control, you can choose to half the damage and then redirect it. Or you can choose to redirect it, and if the recipient of the damage is now an opponent or a permanent controlled by an opponent that damage will be doubled (as now Gisela's doubling replacement effect applies, and not the halving one).
In your example, assuming all damage is being redirected, you (because you are the affectd player) can half the damage to 3 and then redirect it and if it goes to an opponent or his permanent this will be doubled by Gisela (because it is a different replacement effect that hasn't been applied yet), or you can redirect the 6 damage and it will be doubled to 12 (since the opponent as the affected player now, only has one replacement effect left to "choose" from: the doubling of the damage).
Edit: Made a little correction for the case of halving and then redirecting, since there is then another replacement effect applicable afterwards: Gisela's doubling effect.