There is one way you can do it but it will take quite a while.
So, the first step is the catch a bunch of "junk Pokemon" on your Omega Ruby. (To be exact, one junk Pokemon for each Pokemon you are transferring.)
Deposit your "junk Pokemon" into the GTS and ask for the Pokemon you are transferring, let's say a level 22 Rampardos.
Optional: Make your message something like "4 Transfer," this might discourage people from trading that Pokemon, it might also make it easier to find yourself.
Go onto you Alpha Sapphire, then go onto the GTS search for a [your "junk Pokemon" here] with the same gender and level as your "junk Pokemon" on the search screen where it shows all of the trainers who have that Pokemon, click the magnifying glass icon, a screen should pop up. On that screen select the option that says something along the lines of "Search for Pokemon from the same country than yours." (This might not be an option but I know there is an option that says "Search for Pokemon the have a different country than yours.) When you find your Pokemon from Omega Ruby, trade it.
Repeat as said above for each Pokemon you want to transfer.
I told you it would take a long time to do, you probably shouldn't do that because the is one more way you could do, but it is a bit risky, you need a trustworthy Person.
Go on Pokebase's Chat Room and ask if people want to help you transfer Pokemon. When (and if) somebody says yes,exchange friend codes, as you would do for a normal trade. Also tell them how many Pokemon you are transferring.
The person needs to get the same amount of Pokemon as you are are transferring on their game, you also need to do this on your Omega Ruby. This might take a while so be patient.
Optional: Ask them to keep their junk Pokemon in an empty PC box, when you trade Pokemon they are put in the same PC box space as the previous Pokemon.
Start up your Alpha Sapphire and get online, the person who you are trading with should do this too. When you are both online, request a trade. (As with any trade.) Now, trade the Pokemon you want to transfer to Omega Ruby to the person while they trade their junk Pokemon to you.
Get on Omega Rube and get online, request a trade to the person you are trading with, as you would normally do to start a trade. Now, they need to trade the Pokemon you are transferring to you and you trade your junk Pokemon to them.
Make a list of the Pokemon you are transferring so you don't forget what you are transferring and somebody doesn't try to steal one of your Pokemon. Include HP, Attack, Deference, Sp. Atk, Sp. Def, Speed, gender, moves, and nature.
This may be risky but it would definitely be a ton faster than the first way.
Happy Transferring! (Yeah right, it's gonna take AGES.)