You have to be 19 or have a parent's permission to move out. I would talk to them more about it. Yes, Iowa the legal age is 18, but your not a resident of Iowa and I doubt moving their would count.
You are a resident of Nebraska and moving to Iowa will not change that. The age of majority (adulthood) in Nebraska is 19. Without your parents' permission you cannot move out until then. Is your only reason for wanting to move out because they are strict, or is there a more serious underlying reason?
I am a licensed attorney in the state of Nebraska. However, the advice I give here is not to be taken as legal advice. It is merely my opinion based on the limited information given. In order to assure that your legal rights are being properly represented I would always recommend going in for a consultation with an attorney to explain your case in detail and answer any questions the attorney might have.