Can my ex take and move my kids out of state without my consent? If I have any say in it even if there is no custody case and no courts involve?

If your ex moves it could be considered child stealing, but you would be in the strongest position by filing for divorce and custody.

Much depends on what your Final Judgment of divorce states. You should consult with an attorney as soon as possible, as it is easier to keep her from leaving than forcing her to come back.

If you are not married she can move unless you file a petition with the court to establish your rights to the child as soon as possible.

You need to file for a child custody order so that you know exactly when you can have the children. You can always reach an agreement that gets filed with the court and becomes a court order. In it, you need to provide that she gives you 45 days advance written notice of taking the kids out of state (for vacation) with an itinerary and a contact number. Check your documents, you probably each have a right to take the kids on vacation. If it says "travelling vacation" out of state is fine. As long as you know where they are and when they'll be back, the courts would let her go. You cannot arbitrarily refuse to let her take the kids on an out of state vacation, or even out of country.

Assuming you have a custody order in place, she cannot move the children out of state without your permission or the Court's permission. If there is no custody order in place go immediately to the court and file a petition for a custody order. If you wait, she may be able to have the court in the new state take jurisdiction and it will be difficult for you to get what you want. Talk with your attorney.

Your rights as the biological father are determined by the court orders currently in effect. See an attorney with those orders and details for a specific opinion.