Solution 1:

Note the capitalisation of God/god.

  1. I'm neither a man nor a god- man is a countable common noun; god is a countable common noun.
  2. I'm neither man nor God - man is an uncountable common noun designating a class of object; God is an uncountable proper noun, i.e. a name.
  3. I'm neither a man nor God - man is a countable common noun; God is an uncountable proper noun, i.e. a name.
  4. I'm neither man nor a god - man is an uncountable common noun designating a class of object; god is a countable common noun.

You may wish to add

I'm neither man nor god in which both man and god are uncountable nouns.