You seem to have leapt to some conclusions without actually watching the entire series. I see there are other answers that contain spoilers already. I will try to keep spoilers to a minimum, but some are inevitable given the nature of the question.
They are not "illusions." Their nature is left somewhat unclear, but the simplest explanation is (as Head Six repeatedly tells Baltar) that they are angels. Their full level of knowledge or power is never specified, but we know that they can intervene physically when they choose - we witness this when Head Six physically lifts Baltar to receive a beating from a guard (to reinforce his image among his followers).
A (probably) similar being guides Starbuck through the events of Maelstrom, apparently including the ability to travel at will through space and time.
Remember the saying, "all of this has happened before, and will happen again"? My pet belief is that the "angels" are people from past cycles who, through some amount of suffering or learning, attained a higher state of being; I think there is some form of reincarnation in the show; I think we witness Starbuck attain this state during the cycle the show focuses on. However, there's no evidence for that, it's just an idea I like. Many areas were deliberately left unspecified (even the main writers of the show would probably disagree with each other in some cases), because spelling everything out would reduce the wonder and the role of the viewer's imagination.