How on Earth do you guys do it?
Just remember these simple rules of the art of Zombie Fu:
1: Unless it has a gun or is electric, violence with fist or spear is the correct solution. Otherwise, use a gun or non-metal weapon[Fists don't work, even with insulated gloves], respectively.
2: Hitting things is useless without the ability to not be hit. Choose a weapon or martial art with the "Parry" ability. The Dodge skill and/or decent armour also help.
3: You must move fluidly and with great vigour. Avoid over-encumbrance and weapons which often get stuck in your enemy. Spears, blunt weapons and fists work best, especially in the beginning. Many enemies[Skeletons, feral hunters, dogs of all kinds] are your equal or more in sheer attack speed. Being at a disadvantage against them in this regard WILL be fatal.
4: Always be prepared. Carry[At the EXTREMELY BARE minimum] saline solution to wash boomer gunk off your eyes, medical supplies, a way to repair your clothing/armour, a filter or gas mask and at least one weapon to deal with foes rule 1 says you should not hit. Stacking items with high storage[A backpack, a trenchcoat, cargo pants] is a good way to help with this, as long as you don't violate rule 3 with it.
5: Absconding is the best defense. If rule 1 dictates you should not hit something and you lack the equipment to kill it safely, RUN. If the foe you face is surrounded by corpses and is a Lovecraft reference, RUN. If it looks like a dog, but isn't, RUN. You're usually faster then most of your foes and they're not terribly persistent.
There's more advice I'd give you, but these are the most pertinent rules of thumb for dealing with special enemies.