Scenario - Just prior to the New Jedi Order.
The New Republic is innundated by a fleet of organic ships. These are the last remnants of the once mighty Yuuzhan Vong from beyond the galactic rim. After years of fighting they have been crushed by an enemy from another universe. The Negation and their God Emperor
Despite having an irrational hatred of machine tech, the Vong agree to tell the New Republic all they know about the Negation in return for free passage to travel across the void and find another galaxy to settle. The NR agree to share this information with the Empire, Hapans and any other faction you care to name. The SW factions have one year of prep time. For the purpose of this Vs, victory conditions are
Negation
Conquer or destroy the civilisations in the Star Wars galaxy
New Republic
Kill the God Emperor or destroy so many ships and troops that the Negation withdraws.
Numbers
The full extent of the Negation population is unknown. But it is clearly a multi species empire spreading out at least 2 galaxies. It composes the entirety of known space in its universe. But if we make some assumptions like each planet has comparable population to modern Earth, they would have lots of troops to throw at the SW empire. Also assuming they can police their planets albeit sparsely (the Negation does get rebellions) one would still expect lots of industry.
Ship capabilities
FTL - clearly superior to Star Wars as they are transgalactic. A stolen engine on the black market allowed the heroes to go from one galaxy to another in hours.
Weapons - This image gives you an idea of the fire power of their ships. Supposedly they are powerful enough to "set the atmosphere alight."
Endurance - Their ships appear to be able to destroyed by MT explosions, although they most probably have different types of ships. It appears that ships aren't standardised, which makes sense given a lot of the species were conquered.
Wildcards
1. Different universal laws - The Negation hail from a universe where the laws of physics, well aren't universal. That is one sector of space may have one set of rules, another one totally different. As it stands they need to tinker with their ships and Lawbringers to allow them to function in our universe. For the purpose of the debate lets assume that the Negation have worked out how to make their stuff work in the SW universe, and a captured item from the Vong allows NR to work out how to make SW tech work in their universe.
2. Portal - the Negation can create portals to enter the SW universe
3. No other characters from the CG universe allowed. For the purpose of this debate, the Negation invades the SW universe instead of the Crossgen one.
4. Lawbringers - formed from Charon's discarded emotions and merged with the energy of Negation space.
http://en.wikipedia.org/wiki/Lawbringers
The New Republic has its Jedi, but the Negation has their Lawbringers. Rather than me describing how powerful these guys are, let me show you.
Lawbringer QZTR punishes an entire planet for the blasphemy of one citizen.
part one
part two
QZTR getting a hole blasted in his chest
Few other powers a Lawbringer has
Forcefield generation
Telekinesis sufficent to paralyze Several humanoids, some super powered
Teleportation across planets
Firing multiple energy blasts simultaneously sufficient to kill a human easily. Well duh, given what he did to a whole planet.
Oh, and when someone says the Jedi will just TK so that blood doesn't flow into the brain of <insert foe here>, here is the Lawbringer being creative with his TK power. ouch
Here are the Lawbringers in all their glory. At least those ones that haven't turned against the Emperor (of which one is known to have done), killed by Appolyon (a few), killed by the heroes (one). Note there are most probably more than that, and it looked like there were at least a few hundred in the beginning.
5. Super powered troops
Ascended Transitioned humans. Well most probably not as powerful as the Lawbringers, they still pack a punch. To give you an idea of how powerful they are (since I am not going to scan everything in), imagine a Vong raiding party boarding a Negation ship. They surround general Murquade who them pulls out a gun and points to them. The Vong laugh saying that you can't expect that weapon to stop us. Murquade then replies, the weapon is not to protect me from you, but to protect my ship from me. Ship blows up with Vong in it and Murquade survives. This was what happened in the comic, only he was fighting against other Transitioned humans, who combined could easily move like half of a ship. And Murquade was winning before Obregon Kaine taught them tactics and how to outflank the general.
Clearly the Transitioned humans have super human endurance, can survive in space without a suit, energy powers, and they also demonstrate the ability to create "energy chains" to bind captives.
6. The God Emperor himself
The most powerful of the Transitioned humans. Obregon Kaine managed to blast his arm off with a small scout ship, however the Emperor just reattached it. Perhaps his most powerful act is here.
An Avatar of Danik (a Transitioned Atlantean who has been preparing to fight the Negation) blows up an Earth like planet. Not quite a DS level blast because we later do see some parts of the planet including buildings that was somehow survived, even if the planet now lacked sufficient gravity to pull itself together.

The act was not to kill the God Emperor, but his Queen. Danik fully expected Charon to survive. To elaborate further, Danik split himself into several beings to keep an eye of the Crossgen Sigil Bearers, who would be the soldiers he planned to use against the Negation. That means at a lower end, each weak Avatar is at least this powerful, and he must have at least had 10s of Avatars (one for each sigil bearer and two for the First), which are less powerful than Danik himself. Danik fully expected Charon to be stronger than him.
So with all this in mind, what happens. What can the SW factions do against the mad Emperor.