Am I reading this correctly, Grease is not considered difficult terrain? Would this spell work against Huge and Gargantuan creatures if they touched any one of the five-foot squares?
That is correct. Grease is not considered difficult terrain and has it's own specific effect.
By my reading a large or huge creature would make the save so long as a single part if their area enters a single square of the greased area.
Creatures may be able to use the Leap or Squeeze actions to get around without stepping on those squares, though that could slow them down, perhaps less than Stepping.
do they make another reflex save once they stand back up if they fell the first time? Or only if they attempt to move out of the Grease on a different round?
I would rule it that any time they qualify as a creature "standing" on the area they would make the save. Once they successfully save and remain standing they can then step off the surface without making another save, or attempt to stride off of it for at the risk of another save. Once off of the surface they are good to go unless they return to the greased surface, in which case they have to make a another save. It would seem to me that a creature attempting to stand in place over a greased area would make a fresh save every round, similar to how Black Tentacles would attempt to grapple an un-grappled creature every round.
Otherwise there would be no reason to "crawl" off the space in the first place. You'd just flub your save, then stand up and walk off, or stand in place until the duration ends.
Edit: Think of this as a triggered reaction being made by the greased surface. Every time something meets one of the conditions of the spell, ie they are standing on it or trying to stride off of it, they make a save. But the greased area can only inflict one save per "triggering" event.