It means Oh My God.

The Z just adds to the O…like you say Zo (like so) My God.

Its just netspeak

ZOMG is an Acronym. a million. it is a variation of OMG : 2. an magnificent version of OMG used to make relaxing of people. ZOMG is a trifling Enthusiastic / sarcastic way of asserting, ‘OMG’ , ‘Oh My God’. without particular or separate growth of ‘Z’ it could denote to ‘ZO MY GOD!’ too! yet another possible rationalization: “zOMG is a varient of the all-too-uncomplicated acronym “OMG”, meaning “Oh My God”. The “z” became into initially a mistake mutually as attempting to hit the shift key with the left hand, and ask your self “OMG” additionally utilized in all-caps, ‘ZOMG’ is in general utilized in a sarcastic way, in lots of situations a humiliating fasion. it is extensively utilized as a gadget for pointing out the obtrusive.”

ZOMG Zoh My God! (gaming, World of Warcraft)

ZOMG Zombies Oh My God

ZOMG Zeus, Oh My God