I've got question...

I've heard (in the USA):
A: I'm hungry
B: I'm either
Is it correct? Or I have to say "So am I".

What about sentence below:
A: I don't know why he did it.
B: I don't know either/ Neither do I

Or, hmm,
A:I hate chemistry
B: Neither do I / I hate either/ Me too

And the last one:
Jews have their own New Year. And I wanna ask Jew:
Do you celebrate "our" New Year too/either?

maybe in this case I shouldn't use "too" or "either", either (?) (can I say, maybe in this case neither should I use "too" nor "either").

When should I use "too", "either/neither", "so/neither do I" ???

I know, it's pretty easy, but I got lost.
Please help.
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Comments  (Page 3) 
Can I say me either or either do I?
For example...
-I like rock.
-Me either or either do I.
Is it colloquial or completely wrong?
Thank you
They are completely wrong in standard BrE,
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