Learn Italian: Il pesce ha un sapore strano; non lo mangio neppure cotto. - The fish has a strange flavor; I don't even eat it cooked.

In Italian, when a negative word like neppure (not even) comes after the verb (mangio), you must put non before the verb. It is a double negative, but it is grammatically required! If you moved the negative word before the verb, you would drop the non, but here it sits after the verb.

Could I use neanche or nemmeno instead of neppure here?

Yes, absolutely. Neanche, nemmeno, and neppure all mean "not even" and are practically interchangeable. You could just as easily say non lo mangio nemmeno cotto or non lo mangio neanche cotto.

In English we usually say "the fish tastes strange." Why does Italian use ha un sapore strano?

Italian doesn't have a direct verb equivalent for "to taste" when describing how food is. Instead, you say that the food "has a flavor" (ha un sapore). So, "it tastes strange" translates literally to "it has a strange flavor."

Why is lo placed where it is in non lo mangio?