I think the zombies are just human zombies, unless your pokemon get infected and can't get cured because lack of items.
Well we have many times mentioned pokemon getting infected because they were attacked by zombies in this thread. It seems reasonable to assume that other pokemon were infected as well. However due to the effectiveness of flying and such it seems that pokemon lose their superhuman abilities once they become zombified. I guess that this means that a zombie couldn't use psycho shift, but I still think that the zombie condition probably behaves like a status. Anyway this is all hypothetical thinking about an even more hypothetical topic, and thus isn't really relevant.
Sableye: Cut, Rest, Foul Play, Shadow ball. Any held item. Since Sableye is ghost-type it can't die to Zombies, so I teach it cut to harvest lumber as well as to cut the limbs off of any annoying zombies that get too close. Hard to attack me without legs or arms!
Gulpin: Ice Beam, Rest, Strength, Rain Dance. Any held item. Teach Gulpin Ice Beam and use it to freeze those annoying zombies that Sableye doesn't hack apart.
Munna: Yawn, Future sight, dream eater, rest. Any held item. Use it to help me keep rested and on the go constantly as well as keep my other two mons co-ordinated. Yawn, a way to guarentee that animals will sleep, will be useful for hunting wild game if nothing else as well.
My plan is to stake out an area and actively clear it of zombies first with a sizable amount of resources and decently remote before building myself some sturdy walls to keep the zombies out and forming a field to grow crops in. Strength keeps objects from blocking me and, in a pinch, can blockade the zombies out as well, so I'll survive. Could probably use Gulpin as storage but I'd rather get an actual backback. My goal here is more 'long-term survival' than 'fighting a massive horde', especially since the initial wave is the only thing I'm worried about. Afterwards simply built up environmental damage from running into various sharp things just laying around and difficulty in repopulating will keep me safe. Rain Dance can keep my crops watered and potentially allow me to move out into the desert as well (so that the natural heat destroys the zombies).
Keep the zombies unable to even get near me and plan for the long-term. That's my strategy.
The enemy of knowledge is ignorance, not religion.