Dealing with someone who is abusive, can't let go, and even tries to control someone after the relationship is over is a challenge. To begin with, their behavior is unpredictable. So one must expect irrational behavior. That's why the above advice is great. I especially like the "contact" the local women's center and follow their instructions to the teeth" as great advice. I also like the restraining order, notifying the neighbors, and even like in a funny way the "shoot the bastard" part.
There is something that I would add. That is to consider yourself. If you are strong in many ways, and can take charge of things well, then I say stay and fight the jerk. If however, you don't do well at controlling things, then relocating may indeed be best. Sadly it is the recipient of threats and abuse that often pay the biggest price, as our laws, and society don't seem ready to support victims of such behavior.
With 6 sisters and some experience having worked crisis hot-lines, I've seen many of these situations not turn out well for the person being stalked. So do much of what has been suggested, and trust your instincts. If you don't want to or can't fight this bastard, get out of the area, and begin again.
I wish you the best.