I'm not sure if Zapdos can be paralyzed, but I think it might be possible. If it can be paralyzed, you need a move like thunder wave to paralyze. Thunder and thundershock is mostly for dealing damage, so the chances that these moves will paralyze is slim, and probably by the time you manage you paralyze with these two moves, you would have killed the pokemon already.
If the ultra balls always miss, it means that either the health is not low enough, or you need to put it to sleep. Some pokemon that can put other pokemon is sleep are Butterfree, Jigglypuff, Drowzee, Gastly, and their evolved form of course. I think you should probably get at least one pokemon that has the sleep move and it's high leveled, it's going to help a lot when you need to catch Moltres as well.
make his hp really low and take out your strongest pokemon and throw a pokeballl or another one ball, that works for me!
First of all save in front of Zapdos!I am sorry but you are going to have to get a pokemon that knows the move hypnosis. The pokemon that could learn it could be a poliwag. So fist summon out a your strongest pokemon and make zapdos hp to red and then summon out poliwag (make sure poliwag is a high level) and then use hypnosis to sleep Zapdos still keep Poliwag dont switch a pokemon out just in case zapdos wakes up so when zapdos is sleeping throw a ultra ball get at least 15.
Hope this helps, Blazing Kai
The best strategy is to put him to sleep first and then use ultra balls. If you can't use sleep, I would recommend that you save your game right before him and just try and try again until you catch it.