Are the three Legendary Birds from the first generation available to be caught in Pokémon Omega Ruby and Alpha Sapphire? I have been looking on sites and can find nothing confirming that they are catchable in the newest installments.
The Gen 3 remake games contain all the (non-mythical) legendaries of all the generations that were not present in X and Y. Since the Gen1 legendary birds (and Mewtwo) make appearances in X/Y, there is no need for them to make yet another appearance in OR/AS.
These are the only (so to speak) Legendaries you can find in Pokemon ORAS.
The Legendary Birds were available in XY (with Mewtwo), so there were no reason to add them in ORAS, I think.