Use of neither with a list of tensed verbs

There are some related tips, but I did not find any one as this.

The sentence:

1) he considers himself a healthy person because he does some sport and neither smokes, drinks nor takes drugs

According the Cambridge Dictionary website (http://dictionary.cambridge.org/grammar/british-grammar/neither-neither-nor-and-not-either), I suppose that it would be something as follows:

2) he considers himself a healthy person because he does some sport and he does not smoke, drink nor does he take drugs.

I was thinking about these other options:

3) he considers himself a healthy person because he does some sport, does not smoke or drink, neither does he take drugs.

4) he considers himself a healthy person because he does some sport, and he does not smoke or drink, neither does he take drugs.

I have no idea which one is correct or sounds better.

EDIT

Thank you everybody!
Now I am clear with it.

Answer

Number 1 actually looks OK.

In #2, “smoke, drink” s/b “smoke or drink”

In #3, there should be “and” after “sport, “

In #4, it might be better with a semicolon after “sport” rather than a comma, but it’s fine as-is.

BTW: in AmE, one would not literally say “he does some sport”; we would say “he participates in a sport”, or “he plays {handball/hockey/whatever}”, or—if more than one—”he does some sports”

Attribution
Source : Link , Question Author : rellampec , Answer Author : Brian Hitchcock

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