Mr Lance has raised an interesting issue about the use of subject/verb agreement in "neither/nor" constructions.  I would respectfully disagree with:

"Neither the kittens nor the dog is... hungry"

There are at least three individual things which make up the subject and so notionally, the verb should be plural - here "are".  Also, "is" feels strange to my ear.

You could also say: 

"The kittens are not hungry and nor is the dog"   [Now we also bump into subject/verb inversion!]

Yes, you can use it with more than two subjects. 

Eg: 

"I like neither John nor Peter nor Judy."

"I neither like John nor Peter nor Judy. 

*Notice that you have a choice of placing "like" before "neither" or vice versa

Do take note that you must repeat "nor" after each subject you introduce ( NEITHER X NOR Y NOR Z)

Eg:

"We saw neither the plaza nor the coffee shop nor the train station. (Correct)

"We saw neither the plaza, the coffee shop nor the train station. (Wrong)

*Notice that "neither" is only used once, regardless of the number of times you repeat "nor"

I personally like to group singular nouns and plural nouns in a sentence if the nouns are similar. 

Example: "Neither the boy nor the girls are .." instead of writing "Neither the boy nor girl 1 nor girl 2.."

* Notice that the choice of verb depends on the noun after "nor"

Eg:

Neither the dog nor the kittens are...

Neither the kittens nor the dog is...

Lastly, I can simply write: None of the boys was playing in the yard. / John, Andrew and Peter were not playing in the yard.

Hope this helps.
Cheers, Lance