1. If he is not yet inside the house, then you can order him to leave your property. You can also display your firearm to him. If he continues to try to get in, you can aim the gun at him and again order him to leave. However, if he is not in your house yet and has not threatened you with a deadly weapon, you cannot shoot him. You can grab him by the seat of his pants and throw his ass off of your property but you can't shoot him.
2. If he is outside your home and when you approach him he threatens you with a deadly weapon, you can shoot him.
3. If he has forcibly entered your house, you can shoot him. For your own best interests, it may still be beneficial to run him off at gunpoint rather than shoot him but that is up to you. If he has broken into your house and is coming toward you or someone else, you can shoot him. I would avoid shooting in the back especially if he is already heading out of your house.
I believe this to be the correct legal remedies you can take. *Please note that this is not legal advice and I am not held liable for anything said here.