I am trying to pronounce the word neural in an American accent. I found it like nooral. Is that correct? Or should it be like nywral? or something else?
This varies somewhat from place to place in the US. To take another example, "new" is pronounced "nyoo" in some places and "noo" in others. My mother was from the Boston area and she always said "nyoo", whereas the kids I grew up with in northern Indiana said "noo". Whether you add the "y" sound is fairly consistent from word to word in a given place, meaning people that say "noo" will generally say "nooral".
At this point in time, it seems to me that Americans move around so much that it's often the case that different people pronounce it in different ways in the same place.
So, both are correct, the difference is regional, and the regional lines are blurring.