Pokémon games are rarely isolated affairs. Of course, you can trade between Omega Ruby and Alpha Sapphire, but the games are potentially far more compatible than that.
In fact, you can transfer any Pokémon from a core series title, going back as far as Ruby and Sapphire . You can catch every non-Mythical Pokémon between X, Y, Omega Ruby and Alpha Sapphire, but it might still be worth checking your older games for hidden gems.
You can directly trade and battle X/Y players via the PSS. However you must abide by Kalos rules - so no trading or battling with any of the new Mega or Primal Pokémon, any new moves or items introduced in Omega Ruby and Alpha Sapphire.
This one’s easy. After updating Bank to version 1.2 with the online patch (it will be thrust upon you sooner than later), you can trade anything from Omega Ruby and Alpha Sapphire to and from Bank. However no items will be kept in Bank, so be wary (they will be moved to your Bag).
Pokémon Omega Ruby and Alpha Sapphire Special Demo Version
You can send any items or the special Mega Pokémon (Glalie, or Steelix if you live in Japan) to Omega Ruby or Alpha Sapphire once per day. All of this stuff can be obtained in the full game anyway, but if you want an early-game boost, it’s nice.
Pokémon Black/White/Black 2/White 2 (Gen V)
You will need the Poké Transporter app, which comes with Pokémon Bank to transfer Pokémon from any of these games to Pokémon Bank. After that, simpy trade them from Bank to Omega Ruby and Alpha Sapphire.
Pokémon Diamond/Pearl/Platinum/HeartGold/SoulSilver (Gen IV)
You will need two DS or 3DS systems for this and a Generation V game. In the Generation V game, you can use the PokéTransfer system after completing the game to trade from Gen IV to Gen V. Note that you cannot transfer the Spiky-Eared Pichu.
Pokémon Ruby/Sapphire/Emerald/FireRed/LeafGreen (Gen III)
Just a DS and a Generation IV game will do. In the Gen IV game, you want to visit the Pal Park, accessible after obtaining the National Pokédex, so you can trade from Gen III to Gen IV. This is easier in HeartGold/SoulSilver, as you must complete the Sinnoh dex in the other games.