Strictly speaking, only the the first sentence is unambiguously correct:
I can find the tool neither in the kitchen nor in the bathroom.
But what's intriguing to me is the third sentence in which a comma has been introduced. Without that comma, the sentence is unequivocally wrong. But a comma can be used to separate two independent clauses. Combine that with the concept of elision, and the third sentence could actually be interpreted as:
I cannot find the tool, it is neither in the kitchen nor in the bathroom.
I dislike that punctuation and I would either use a semicolon or make it two sentences. But if the sentence is interpreted that way then it only has a minor punctuation issue, while the use of 'neither' and 'nor' is actually correct.