Ninja will require of you to be allied with a Japanese city-state, have certain social policies unlocked and certain technologies researched. It will be able to enter tiles occupied by other units, perform spy-like missions and be invisible until it attacks.
Pirate will be a land version of Pirate Ship/Privateer. It will act like a reverse transport – a Pirate Ship may enter a coastal tile and turn into a Pirate (it cannot venture further inland). Pirates, like Pirate Ships will have hidden nationality.
Zombies will be created from units placed on tiles next to a city with a Nuclear Reactor when it meltdowns. They can cause defending units to run away to unoccupied tiles, heal from victorious combats (by feasting on the dead), and have a chance of turning defeated units into Zombies.
But none of the above is the secret unit. The secret unit is a Zombie-Ninja-Pirate, created when a Ninja and a Pirate stand on the same tile next to a city with a Nuclear Reactor during meltdown. Zombie-Ninja-Pirate has all the abilities of Zombie, Ninja and Pirate (including an ability to become Zombie-Ninja-Pirate Ship, and turning defeated units into Zombies).