I am not Norwegian, do not know how to pronounce this name, and have never seen an 'O' with an / through it. This name is so cool though, that I felt I needed to comment. Ya BJORG!
I am Danish and the letter ø - which is a Danish letter (surprised, btw, that Danish isn't listed as a nationality on this name) - in Bjørg is pronounced like ö in German. I like this name.