–IVs can be checked in XY at the Kiloude City Pokémon Center. Talk to the guy with purple hair on the left, referred to as the Judge, and he'll list one or more stats, and then either "decent," "good," "fantastic," or "can't be beat." He will
only list the stat(s) with the highest IVs, so you'll have to go to an online IV calculator to find the rest (just Google search for it). You want the stats to be "can't be beat," which would mean that each of the stats he listed has an IV of 31. The same judge can be found in ORAS at the Battle Resort (I think also in the Pokémon Center).
EVs, on the other hand, are a little more tricky. The best way to check would be to go to Super Training, save the game <-(this is very important), and then use a Reset Bag on the Pokémon whose EVs you want to check. It'll take away all the Pokémon's EVs, but it'll show you how many it had before taking them away. It only shows them for a few seconds, though, so I recommend having a camera on hand. Afterward, you can restart the game to the point where you had saved, and the Pokémon will still have its EVs, only this time you'll know how many EVs it has.
The absolute easiest way, though, is to start from scratch with a Pokémon you know has 0 EVs, like a freshly hatched/caught Pokémon. Then, you can just keep track of how many EVs it gains.
The easiest way to EV-train a Pokémon is by using hordes, Pokérus, and Power Items. Hordes, as I'm sure you know, are groups of five of the same Pokémon, so you'll basically quintuple the EVs gained in each battle. Pokérus doubles it further, and Power Items (Power Bracer, Power Lens, etc.) add 4 EVs to the specified stat, before multipliers.
So consider, for example, that you wanted to train an Abra in Special Attack. You would first give it Pokérus (you have to have another Pokémon with Pokérus for this, just Wonder Trade until you get one if you don't have one already. It's characterized by a bar saying "Pokérus" under the Pokémon's name in the summary screen) by having the infected Pokémon in the lead slot of the party, Abra in another slot, and the Exp. Share off. That last part ensures that the Pokémon doesn't gain unwanted EVs prematurely. Then battle until Abra is infected with Pokérus.
After that, give Abra a Power Lens (obtained at the Battle Maison) and fly to Hoenn Route 119. Make sure you have a Pokémon with Sweet Scent in your party
or a ton of Honey, as well as a Pokémon that has a multi-target move (Surf, Earthquake, etc.) in the front slot. Turn the Exp. Share back on. Now use Sweet Scent or Honey to attract a horde, which should be Oddish. KO all of them with your multi-target move (be it Surf, Earthquake, or other). Now, here's the calculation for all the EVs Abra gained:
1 (Oddish gives 1 base SpA EV)
+4 (Power Lens)
x2 (Pokérus)
x5 (you KO'd 5 Oddish)
Total:
50 SpA EVs
And the table for which Pokémon give which EVs is as follows:
HP: Whismur (Rusturf Tunnel)
Attack: Shuppet (Mt. Pyre)
Defense: Sandshrew (Route 111)
Sp. Atk: Oddish (Route 119)
Sp. Def: Swablu (Route 115)
Speed: Zigzagoon, Taillow, or Wingull (Route 104; all are on the route, and all give 1 Speed EV)
–Cosplay Pikachu
can have max IVs in every stat; you would just need to soft-reset for them (Google search the term if you aren't sure).
As for the EVs, only you can control how many EVs it gains, so yes, it can have max EVs, and will, unless you never use it for battle.
Hope that helped!