Armadyl - Weak and powerless because he has basically no following and lost his staff. If he comes back he'll either be killed quickly or no one will really care enough about him to do anything
Bandos - He just likes to have fun. He is more powerful than his minions, so he does what he wants to them. He believes that the powerful should rule, which is probably the most natural and most easily enforceable. In a way, he's a lot like Zamorak, except he doesn't necessarily use his chaos for good. Regardless, he keeps the lives of his minions interesting and eventful, giving them a meaning in life.
Saradomin - Basically a mockery of the Catholic church. He has goals (were they ever revealed?) that he will do anything to achieve. My guess is that he wants to be the only god so that he doesn't have to share power. Mortals are merely pawns to him, he doesn't see them as living beings like himself. He will lie to them, cheat them, and abuse them for the sake of his goal.
Seren - She loves her followers immensely. They're all that matter to her. She only wants what is best for them. She has a very specific idea of what is "best", though. Peace, isolation, freedom. She fails to see that this leads to the monotony and meaninglessness that found Zamorak's beliefs. It also seems that unless a follower truly loves her, he or she will get nothing from her.
Sliske - A wildcard. He may have had contact with Zaros, if he can actually travel to the Shadow Realm, rather than just disappearing and reappearing somewhere else. His motives and goals are a mystery. He's very intelligent, selfish but loyal, and very powerful. Siding with him is a gamble, either he will forsake his followers and follow a selfish desire, or he will award those who aid him magnificently.
Zamorak - He believes that chaos brings meaning to life. Without it, we grow complacent. We never stop trying to improve ourselves, our society, or our world. Yes, there is destruction, but it fosters growth and society becomes stronger. We see this in the real world as communities form strong bonds after disasters. In a way, he wants what is best for everyone, not just his followers. He knows that he must provide an impetus for humanity to grow. If Seren were in control, life would be meaningless.
Zaros - He just wants power. He seems to be very similar to Saradomin, like pretty much exactly the same. In the modern age, we think of him as deceitful and evil, but Saradomin was as well. Saradomin just managed to maintain a reputation of wholesomeness and justice. Zaros probably lied to his followers as well.
The Godless - They have a lot of things right, especially how gods only cause war and destruction. The teachings of Zamorak say that this isn't a bad thing, though, because it creates progress and meaning. The beliefs of the Godless seem to be based around the short life spans of humans, where "the greater good" has no meaning to them, because benefits are only seen generations later. It is unlikely that this faction would garner support from any major creature other than humans for that reason.