GED is a bit of paper in the US saying you have, what is legally considered to be, a high school diploma. However, the GED is not the same thing as a high school diploma. I'm not saying it is not as good, just different.
Also, having reread your post, instead of contacting embassies and consulates, try the language school and or university you are looking at. Since they will be the ones to sponsor you, they are the ones who will decide if your GRE is OK to use. Sorry about that...