WOW...I could really go on a long Collin Powell on this Thread. But, I'll try to keep it short. I see what the issue is.
First, You are working according to a rule you learned in Cali, and now you're in NYC. The problem is he doesn't know anything about your rule, or that this rule you are judging him on even exists. He probably thinks that you're testing him in some other way, and he's trying to show determination. Is is possible that you made a really good impression on him
Second, You are doing something many women do. You haven't made him aware of what his position is. So he's calling to get some idea as to what his next move should be. It's obvious that in the time you two did have to talk you were ever straight and direct about what kind of position you had open and what the rules of that position was. He's like a basketball player on a football field. He has no idea of what the boundaries are and what he's supposed to do, so he's doing the only thing he can.
Third, You haven't made him aware that you have objections to him calling you. You haven't explained to him that his voice mails are bothering you. Since you haven't done that , how would he know this is not something you want. Especially if you've talked to him after he's called a few times. You've pretty much support this behavior. If he's called you 10 times, and you've picked up the phone and had a conversation with him and didn't tell him that calling you 10 times was extreme, that's your fault for not speaking up.
I'm with everybody else here in this thread that says if you're no interested in the guy then you should be woman enough to let him know, that way he can move on to some one , with whom he has more potential. I think every man in the world has been in this man's shoes. So we are telling you the truth. Either you are interested or you're not interested, what ever it is just woman up and let him know what the deal is.
True you said you're very busy, but what does that mean? Did you tell him not to call during your work hours? Did you tell him that you didn't like voice mails? "I'm very busy" is a vague statement.
You can't expect him to live up to or meet your standards, when you haven let him know what they are. Also, Why are you so bothered by voice mails, and calls? You gave him you phone number, did you not think he was going to call? If Voice mails and calls bother you that much you may want to be more selective on how you give your number out. Remember, you gave him your number, he didn't steal it from you.