So, I can use "either ... or" and "neither ... nor" with more than 2 objects and I have two choices: 1) duplicating "or/nor" before every object 2) duplicating only before the last one

1) He knows neither me, nor you, nor her, nor them

2) He knows neither me, you, her, nor them

3) You can call either me, or my brother, or Geroge.

4) You can call either me, my brother or George

They all are correct?

Correct!

What about "both ... and"? Can I say

1) I called both Jerry and Larry, and Martin, and Walter

or

2) I called both Jerry, Larry, Martin and Walter

?

That doesn’t work because BOTH implies two people.

What to do then? Only with commas?

I called Jerry, Larry, Martin and Walter

Only so, no other way?

Yep, that’s the only way.

Or you can put AND in front of everyone.

In front of everyone?

I called and Jerry, and Larry, and Walter and Martin

Is it English? :D

I called Jerry and Larry and Walter and Martin.

[no commas]

It would sound alright?

I wouldn’t give it to you if it wasn’t going to sound alright))

Logically))

Then what is the difference between

1) I called Jerry and Larry

2) I called both Jerry and Larry

The word BOTH - otherwise the meaning is exactly the same

Okat, understood, thanks!
By the way, why did you write

"I wouldn’t give it to you if it wasn’t going to sound alright))"

Why not "if it weren't"? As far as I know conditional sentences include "were" for any pronoun

You can use WEREN’T or WASN’T - the latter sounds more “normal “

More normal? But how does "weren't sound"? Informal?

No, more formal

Oh, interesting. You are going to be my English Guru=)

Cool!