The phrase is very informal and can sound offensive, better used among close friends. We were joking around and I told my best friend to eff off when he teased me.
Pro Tip 2/3
Intensity
It expresses a strong desire for someone to go away, carrying more force than simply 'leave'. She was so irritated with the salesman that she snapped and said 'eff off!'
Pro Tip 3/3
Anger Expression
It's often used to show anger or frustration towards the person being spoken to. After losing his patience, he shouted at the noisy neighbor to eff off.