You guys are thinking it all wrong.
You shouldn't waste your time trying to kill them, there's just too many. Your number 1 priority is to stay alive. Therefore the best 'mon suited for the job is Zoroark (assuming his illusions works on zombies). Travel to the woods and the wilderness, where less zombies appear, beneath the cover of Zoroark's illusions.
The next thing you should do is find other survivors. It's humankind's only chance. Find enough people to form a solid society. Find a safe to construct your hideout. Make sure to be on a lookout for zombies approaching, and only when they are should your Zoroark cast his illusion, so he saves energy for emergencies. Divide your men to gatherers, doctors, make some form of authorities and law enforcers.
Once your society grows in numbers, send small groups of men to look for other survivors. you shouldn't place all your people in one place, in case your hideout is wiped out or is contaminated. Make sure to keep the women safe, and start breeding like hell. Also, be sure to keep contact with your exploration groups. Communication systems, and other forms of technologies in general are extremely important for survival. Be sure to use radio transmissions to locate other survival groups, make your presence known in traveling individuals trying to find a group and boost morale among them.
Gather knowledge. Keep any scientist you find safe. Find a way to massively destroy zombies or find a cure to the zombie pox. If the internet still works, it's a huge boon. If not, try to preserve as many books as you can, so not all of mankind's knowledge is lost.
You should prepare yourselves for when the babies start to come. Make sure to have as much medical knowledge as you can in order to have a safe labor. When they grow, prepare them for what's out there.
Other than that, wait. Assuming zombies don't breed, they will eventually wipe themselves out. you're goal is to form a safe society that is capable of surviving and preserving mankind, and it's knowledge, enough time for the zombie apocalypse era to end.
The fate of all mankind rests upon your shoulders.
And may Arceus help us.