We have used the Edison to get data from a MPU9250 9-axis motion sensor. Here is the repository where the Arduino sketch lives.
You could consult the read/write function to see how to interact through the Edison with the GY-80. It should be straightforward to use the Edison in place of any Arduino you were using. Here is an Arduino sketch for the GY-80:
Just remember though, if you are using the mini-breakout board, you will likely have to level-shift the digital signals since I don't think the GY-80 is 1V8 compatible. In other words, don't send 3V3 (or, gasp!, 5 V) signals into the Edison IO ports!