If my ex-husband lives in my house but there is no rental/lease agreement and he pays no rent, can I enter the house without his permission?

Hello. I do not understand why a man is living in your home with no agreement.  Did you mean there is no written agreement? Is there an oral (spoken) agreement? A wriiten lease is required by law in Minnesota in certain circumstances only. Or, did you just learn that the man is 'squatting' or 'hiding out' in your house?  Regardless of circumstances,  I recommend you seek counsel of a private attorney regarding your situation right away. I recommend that you make several phone calls to attorneys in choosing an attorney, because you should feel great trust in the attorney-client relationship. All the best.