Is Nvidia Optix, Nvidia Hairworks, and Nvidia Waveworks compatible with UE4?

UE4 will take care of specific OS files when you publish your game to a specific OS to run the game on it

For consoles suport you need to be registered developer to publish on those.

So no. You dont need CUDA.

As for OptiX. It is realtime simulation. If youre refering it to Vray and mentalray well it is more like V-Ray RT and Nvidia IRAY in 3dsmax