I was in a similar situation until a few weeks ago - with me having to turn off my phone, block him on msn and with him creating new accounts and trying to trick me into talking to him, etc etc, even though I was clear how I felt. He started hanging around near my house - he even came to my church and tried talking to me through the vicar! (This was after us breaking up and deciding ''to be friends'' and then a bunch of crap happening).
After like 2 months of this I'd really had enough, and I understand how disruptive and annoying it can be. Like the OP I just don't know why he was doing it seeing as it was bad for both of us.
Anyway it's a lot better now - I think you do need to give way a bit, stop the threatening emails, and talk a bit to her, even if it's just on msn. If you try to keep it civil, you might be able to resolve some stuff without it turning into a massive argument. I just think if you do have at least some contact then she won't be so obsessed with trying to get hold of you and will stop calling you at work etc. That's how it seemed to work for me.
For me, the whole ''cutting off all communication'' seemed like a good idea, but it just didn't work, because there was always some way he could contact me, which made me nervous all the time! But maybe it's different for you since she lives really far away?
And I do think you should say something to the new girl just to avoid nasty surprises.
Sorry about the length of this post