Okay, here's the scoop...
The detective called me this afternoon and told me what's going on. Evidentally, the phone number goes to a server where the phone call is directed to whatever "free" phone call the dialer has dialed. He spoke to the Director of Operations of a company called Oovoo. The guy wanted to speak to me.
He was very apologetic and explained exactly what was happening. I told him I was more annoyed than anything else, given the hour of the calls, and the vileness of them.
This company is in the process of offering "free long distance calling". Whackjobs are signing up and calling all OVER the effing world!! The phone call that pops up is Oovoo's server, so you can't call it back.
He told me next month they are going to start charging subscriptions and also cancelling the free calling.
At least now I have an explanation. I thought, "Hmmmmm, class-action suit anyone????"