I'm no expert on this, by no means. But what I read is that the border between Europe and Asia is not so clearcut everywhere (cultural, political and geological factors can play a rol).
As to Georgia, since I grew up hearing it's more European, I had to look it up when you mentioned Asia. It seems that just a few provinces (called Khevsureti and Khevi) are European. I must admit, I don't know why these are European, I guess it's historical. But I guess that me thinking it's European has more to do with the country's attempts to become (politically) part of Europe.
as far as seven continents: yes that's what I've learned too, but it's up for
debate.
(everybody bored yet..?

, PNA and I will open our own geography thread soon..:greenpbl
pascal