Hatenko: In my opinion, the order of importance is: EVs, Nature, and IVs.
EVs: Up to 252 EV points in one stat, so an overall 63 stat point point increase; Up to 510 max EVs, so an overall 127 stat point increase.
Nature: 10% increase/decrease, so an overall 30-40 stat point increase/decrease for the corresponding stats.
IVs: Up to 31 IVs in one stat, so an overall 31 stat point increase (however, if all 6 stats have max IVs, then it would have an overall 183 stat point increase... Although it is unlikely to get a Pokemon with all 0 IVs anyways, so you should get mediocre IVs unless you rebreed).
mic000899: Yes, if Pokerus is cured, the Pokemon will still gain twice the amount of EVs. Pokerus disappears from your party Pokemon once the in game clock hits midnight. However, if you deposit the infected Pokemon in your PC before midnight and withdraw it after midnight, it will have Pokerus forever.