I dont think its poswsible for the Eldar to completely kill Slaanesh. Once something like that has been created, it would nigh-on impossible to contain it.
if the Necrons got completely wiped out, you can say goodbye to the rest of the Galaxy - the wierd pillar things (cant remember name) on Cadia that are holding the Eye of terror in check are Necrontyr contructs built as a permanant way of holding back the Warp, the main enemty of the C'tan. But they are powered by the life energy of the C'tan, so if they die completely, which is unlikely, Cadia will fall, and the Eye will spew forth an unquenchable army of Chaos.
This also links to the Eldar who, i they are ever completely destroyed, will release the power of their God, Khain, which will immediatly target the Necrons, being their origional enemies, killing thm all and subsequently realeasing the Eye of Terror (which they ironically created.)
Orks and Nids are the most and least lkely to win the galaxy, depending on which way you look at it. on one hand they have enough warriors to completely overrun everything in the Galaxy, but they are also two of the most phsycically powerful races, as well as the Eldar, so any fluxuatins in the warp will affect them, and if the Warp is completely cut of from the material world, all three of these races will suffer the most.
the eldar will not be able to communicate or see into the future etc.
the Nids' hive-mind will not be able to communicate with the Hive Fleets, and they will fall into disarray, althought they will still be a force to be reckoned with.
the orks are the most interesting - the only thing that keep any of the Ork Meks inventians (Tanks, Guns etc) is the psychic power of the Orks aroun d them. they belive that they will work, and so they do. but if you take away the Orks subliminal psychic bilities, they will not have the power to sustain the weapons etc and they will just fall apart. this will deprive the orks of long ranged weapons, space travel and basic transport, effectivally rendering them useless.
this is why i love the 40k universe, and the amount of thought that GW has put into this to ensure that no single race can ever reign supreme.