I've only ever heard Old Timers use the term "New Order."
Growing up in the 80's thru 2000 it was always "The New System of Things."
In fact, you could gauge how old or rather how long a person had a been JW by the term they used. If someone used "New Order" you know they were either old or in long enough to have studied those older publications because they used it. I'd guess the "Live Forever" book is the publication that got "New System of Things" really rolling and it stuck the longest.
I've never heard any JW's used the term "New World Order", UNLESS they were referencing something some political outside that was being discussed at the time. Like George Bush using it, or in relation to the United Nations, etc. The closest thing to that in JW-terms was the title of their bible, "The New World Translation of the Holy Scriptures", which was pure garbage according Dr. J.R. Mantay. (whom WatchTower misquoted about the deity of the Christ.) Source: the 1986 documentary, "Witnesses of Jehovah" where he was interviewed.
On a similar tangent, we could start a thread about the evolution of this cult's name throughout it's existence:
1. Bible Students
2. IBSA
3. Jehovah's Witnesses
4. The WatchTower Society of Pennsylvania
5. The Society
6. The Organization
7. The Christian Congregation of Jehovah's Witnesses (mostly seen on WT letterhead correspondence)
8. JW.borg