Is there at least one right sentence on the list?
1) You should say it to no one
2) You shouldn't say it to no one
3) You say it to no one
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Yes! Your first and third statements are grammatically correct.
So your first sentence means: You should say it to nobody.
As it is constructed it may convey any different emotional part of politeness, advice or a hint.
The second sentence sounds more like an order or a command. It implies more rudeness.
On the other hand as Chris M advised the better option might be:
Depending on your emotional choice the right formulation might differ.
Your third sentence: You shouldn't say it to no one.
That is a double negative which certainly implies an opposite meaning:
Double negatives are to be avoided in English and are counted to be grammatically incorrect though I personally often times ignore this myself and find some examples of using double negatives absolutely and logically correct. But this is my personal point of view.