Seems this sort of thing has actually occurred, particularly in Australia. We read an article about it. What is happening is people like to keep birds like Amazon parrots and African greys as pets. They care for them, feed them, and teach them to mimic simple words like "hello", "good-bye", and sometimes other colorful phrases that would not be appropriate to share here. Despite the care these birds may receive some of them manage to escape to freedom. Once outside they join their wild counterparts and eventually these birds pick up on the words and phrases and start saying them also. In addition to this the offspring of the escaped birds also can learn them. It becomes a part of the flocks "language" and can even be passed on to other parrots or cockatoo flocks. Evenually an entire forest could be alive human language. So next time you're on a stroll and you hear a strange voice, consider looking up. There just might be a bird up there and it might have something important to say.
Here's a short and humorous video we found on how to train a bird to talk.