Although I am not of the "Norther Tradition folk", I am Scandinavian and have heard the story of Odin sacrificing his eye many times.
My grandmother used to tell me that story when I was little, and she always said it was his left eye. When I asked her why, she said it was because he was right-handed, and didn't want to give up his right eye. If this is true, I don't know. I only have her word for it.
Doing a bit of research on google images, most pictures shows him with only his right eye. There are a few showing him with his left though.
When I looked it up on wikipedia, it said that it is unclear which eye he gave.
I hope this helps a bit.