Do multiple defense buildings stack? As in is it worth having more than one of them? Also, is it worth not deleting my old obsolete ones when I build a new shiny one next to it?
Also if they do stack how many total defense points are enough to make sure I am basically OP and be boarded?
They stack additively. By default, each defensive building fires once when your base is assaulted.
Additionaly, each Grav Shield adds a round to the landing phase, allowing all weapons to refire.
The big question is whether UFO's armor counts during the landing phase.
If it does not, the beefiest craft that is going to attack you is the Battleship with 4000 health.
So I'd say that with 8000 adjusted defensive points (Defensive power * accuracy) for low accuracy weapons, or 5000 adjusted defensive points for high accuracy weapons, you will be safe. If a weapon was guaranteed to hit, then 4000 defensive points would be always enough.
If armor counts, it is not so simple. In such case, you would get more use out of high-powered defenses, than out of low powered.
A battleship has 60 Armor. So if it counts 3 400 strenght defenses will deal 1020 damage, where a 1200 strength defense would do 1140 damage (assuming all hit in either case).
With 3 Fusion Defenses and 1 Grav shield, a base should be almost completely safe either way.
With Missile Defenses, I'd say you would need to have 16 to be completely safe (or 4 MDs and 3 Grav shields).