Can I legally move my son out of state at the age of 16 without his fathers approval? My son and I want to move to Wisconsin and we currently live in California near his father.

No, assuming the father has and is using his visitiation you will need his permission

1. if it is written in the child custody agreement, you will have to or it will give him the right to ask for custody of the kids or to force you to move back

2. if not in the agreement, he may file a motion in court to prevent you.

So
1. does the father regularlly see the child
2. is the father current or close on child support
3. will father object to the moving

If the father is regularlly seeing the child, what accomidations are you willing to make to give father chances to see child.
More visits at holidays and summer with you paying for the transportation ? Perhaps