Ain't no thang! ...or is it?
Retina, 63 bytes

No,

Mi`\bn(e(ith|v)er|o(|body|ne|r|t|thing|where))\b|n't\b
0|2


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Explanation

No,



Remove No, from the input. Due to the capitalisation rules, this can only appear at the beginning of the input, so we don't need an explicit ^.

Mi`\bn(e(ith|v)er|o(|body|ne|r|t|thing|where))\b|n't\b


Count the number of matches of the case-insensitive regex after the `. It just matches all the relevant words, where I've extracted common prefixes/suffixes with the alternatives.

0|2


Count 0 or 2s, so we turn even counts into 1 and odd counts into 0.