Yes he can. Nothing to stop him except for impeachment.
But:
- If they are illegal, they will be challenged and the courts will put a stop to it. You saw it very quickly with the stoppage of the immigration ban this weekend. What trump signed (stopping legal residents at the border) was clearly illegal. It was also ill thought out and not executed very well, made him and his team look ridiculous which you can read more about in that article.
- The states can resist and can easily ignore since the states (for the most part) control enforcement. eg : I expect he will pass a series of "illegal alien" orders. I expect none of those orders will be enforced in California.