Use of not, nor and neither, nor in sentences

No. To use "nor" there, you'd have to start "I eat not apple, nor banana ...." The thing is, you'd sound like Hamlet.

I don't eat apples, bananas, oranges or pineapples.

Thanks mate.

Are these fine now?

I eat not apple, banana, orange, pineapple.

I eat neither apple, nor banana, orange, pineapple

Not at all. They are bizarre.

The first is right out. The second uses "neither" for more than two things, which many people don't like, and the list trails off in an unnatural way.

Thanks again.

For me the following sounds natural and I used to write like this very often for three things. But after reading your replies, I feel I was incorrect. Can you confirm this?

I eat not apple, neither orange, nor pineapple.

That sounds like if Tarzan went to college.

Thanks.

Then how would you write for such three options?

I do not eat apples, oranges or pineapples.