In the United States, you can say either "oh" or "zero." "Nought" is understood but not used. Thus in the U.S. (2) and (3) are both correct. I think it would be more natural to stay consistent, though, and use either "zero" or "oh" throughout, so it is more likely that you would say "zero point zero zero one" than "zero point oh oh one." You would not use (1) because it does not correspond to what is written. You would only use "point oh oh one" if the written form really was ".001" without a leading zero. We are taught always to write "0.001," never ".001," because the period is inconspicuous and easily missed, and the leading zero makes it more visible and avoids transcription errors. In real life depending on the situation, if you were reading it aloud for people to listen to, rather than dictating for transcription, one might read "0.001 inches" as "one thousandth of an inch." One might read "0.001 liters" as "one milliliter."

You can say "zero point zero zero one". Or "nought point nought nought one". In maths and science now we are told not to omit the "0" before the "." We only use the letter "o" to represent a number when we are saying a telephone number or a road number.