First: The NWO is the New World Order, the 1984-style global prison that the Illuminati are trying to persuade us to accept.
Second: The Illuminati does exist; it has been mentioned since ancient times and continues to be so today. It is not secret; they prefer distraction to supression because it's much more effective. It goes under names like "the men in grey suits" and "the olympians". It's unlikely that they call themselves "the Illuminati".
Third: The European Union is designed to be one of the three divisions of the NWO along with NAFTA and APEC. (I don't include the OAU becuase the Illuminti plan to kill everyone in Africa)