I'm not sure why you bring up "Obama" and point at his EO, where an acting president just did that recently, cough, cough "Protecting the Nation from Foreign Terrorists Entry Into The United States".

"Executive orders are orders issued by United States President and directed towards officers and agencies of U.S. federal government. Executive orders have the full force of law, based on the authority derived from statue or the Constitution itself."

Looks like it is derived from statue or constitution and they do have the full force of law, are they lawful and constitutional? That's for courts to decide.