Name collision, read carefully: “The New Jedi Order” here means the Del Rey book series of 1999–2003, set 25–29 ABY in what is now Star Wars Legends. Lucasfilm has since reused the same phrase as the name of its ninth official publishing era, which sits in current canon after The Rise of Skywalker and has almost nothing published in it yet. Same words, different continuity, different century.
The New Jedi Order is the most ambitious thing the old Expanded Universe ever did and the reason a certain generation of readers is permanently unimpressed by lower stakes. Nineteen novels, a dozen authors, four in-universe years, and a genuine willingness to break its own toys.
The invaders
The Yuuzhan Vong come from outside the galaxy. Their technology is entirely biological — ships, weapons, armour and communications are grown rather than built — and, crucially, they do not register in the Force. A Jedi cannot sense them coming. That single premise dismantles thirty years of accumulated Jedi advantage in one move, and the series spends nineteen books following the consequences honestly rather than reversing them.
Their religion is built on ritual pain and self-mutilation, and their central objection to the galaxy is not political. They regard machines as abominations and the Jedi as the galaxy's chief blasphemers. There is no negotiated settlement available for most of the war because there is nothing to negotiate about.
What it costs
Chewbacca dies in the first novel — Vector Prime — crushed by a falling moon on Sernpidal, and the series makes it clear from that page that nobody is safe. Anakin Solo dies at Myrkr. Jacen Solo is captured and tortured for months. Coruscant falls and is terraformed into something the invaders name Yuuzhan'tar. The New Republic itself does not survive as an institution — it is reconstituted mid-war as the Galactic Alliance.
Why it is worth reading
Because it is a war novel sequence rather than an adventure sequence. The quality is uneven across nineteen books and a dozen hands — that is unavoidable — but the peaks are extraordinary. Matthew Stover's Traitor (2002) is a philosophical two-hander about a prisoner and his interrogator that has no business being this good. Troy Denning's Star by Star (2001) is the series' pivot and the darkest thing published under the Star Wars name until then. James Luceno's The Unifying Force (2003) actually lands the ending, which almost never happens.
Continuity status
All of it is Legends, and none of it happened in current canon. Rey's galaxy has no Yuuzhan Vong. This matters less than you would think: the series is closed, complete, and does not depend on anything outside itself. It picks up from The New Republic and hands on to The Legacy Era, and those three pages are the whole Legends post-Endor spine.