The Great Hyperspace War laster less than a year I think. It is testament to Naga Sadow's ferocity to cause such damage in such a short amount of time. It lasted between a few days to a few months and cost many lives.
Many of the remaining Sith were killed at the planet we now know as Nathema by a Sith Lord called Vitiate. The remaining Sith followed Vitiate to Dromund Kaas to rebuild their Empire, which was later discovered by Revan and Alek before the Jedi Civil War.
So the supposed "genocide" commited by Republic (or even Jedi) didn't actually happen? (The timeline videos and some NPCs in the game seem to imply this genocide.)