In Classical (Greek and Roman) mythology,the Styx is the river that separates the living from the dead. It is the river that separates the living from hades (hell).
The expression "out in the Styx " means far away from civilization, where nothing much happens.
The spelling "sticks" is incorrect. It should be "Styx".
Hey dude, I'm living out in the Styx. Nothing happens here - not even shit!