I agree with Beagle and have a question for him.
You say the virgin birth is a Greek concept, would the greeks have seen a god having child with a human as "virgin birth"? Also, why would they care? They didn't seem overly concerned with virginity.
My comment was aimed more to the Greek concept that gods mated with humans all of the time, and indeed, if you didn't have a god as one of your parents, you weren't much of a famous person.. This, I believe, would have been sacrilegious to Jews.
I'd have to research this more, but IIRC, the virgin thing came from the Septuagint, the Greek translation of the Old Testament. In trying to proof-text "prophecies" from Isaiah and other OT, they used a reference that most modern scholars say should have been translated as "young girl" rather than "virgin."
So the two memes merged.
I lived the skit (Monte Python, I think) where Jesus is protecting the adulterous woman, saying, "Let he who is without sin cast the first stone."
Then a stone come sailing at his feet, and Jesus shouts, "Mother, go home!"