Demons aren't malevolent independent entities.
Demons are (by the most prominent theory) portions of the human mind responsible for the manifestation of certain mental abilities. To a certain extent, most of these demons overlap and share abilities with one another, covering about seven or eight major categories of action. All these categories break down into either telekinetic or telepathic abilities.
What is a demon's agenda? Simply to operate according to its nature. When an imbalance occurs in the host mind and a demon is actually responsible for conscious behavior, the problem of possession occurs. Demons are incomplete consciousnesses and are naturally incapable of competently performing all the functions of the conscious mind.
This is where that pea soup thing comes from.
There is no "agenda"--demons who find themselves suddenly able to drive the bus are just plain likely to drive right off a cliff, not knowing any better.
Demons come from a realm just as unexplained, frightening and dangerous as hell. Just because they come from your unconscious mind doesn't mean they can't destroy you.
I always teach students that it doesn't really matter if demons are "Demons" or "Brain-Goblins", most of the rules apply to both. The difference is that there are far fewer limitations on "Brain-Goblins". For example, two people can call the same demon in two places at the same time, two different manifestations of the same demon can give different responses, possession can be cured by damn near anybody.
Okay that is one theory and beautifully articulated by Lud. It also happens to be the theory I subscribe to, but I should probably give equal time here to the other view that a demon is a separate entity. I'll leave the theological trappings out of it and you might be able to see why the mechanics work regardless of the belief.
Theory two is that a demon is a preternatural sentient intelligence. Preternatural means that a demon never was alive and is not bound to physical laws. A demon, therefore, has no timespace limitations. That is where you get telekinetic and telepathic phenomenon - the demon's knowledge is not bound to a conscious mind or time or a place.
What a demon lacks is being. The agenda of possession is the attainment of being. Being is something a demon cannot accomplish on its own. The most attractive package for being is humans as we are the highest order of species going on around these parts. So the demon invades and takes over being. (Classic theology will tell you this is in defiance, imitation or abomination of the source of being, i.e. the creator)
Access to being requires overriding the will of the being. So there is a long process of courtship and breakdown of the conscious and the will of the host. A demon is a parasite in this sense.
Once possession occurs the results are exactly as Lud described them. However, most of the truly freaky stuff doesn't come out until someone tries to dislodge the demon. At this point the demon will fight like any animal to maintain its being. In possession cases a demon will risk the death of the host to maintain being. This makes no sense to us, of course, as the death of the host means the loss of the being/locus. But that just tells you
that the locus is more important than the host. That is the agenda - the agenda is "to be".
Exorcism involves dominating the demon by authority. Under the separate being theory the authority is another higher separate being (god). Under the atheistic view the authority is the part of the person's psychology that is the higher, ordered and actualized will. The results are the same.
As a demonologist I tend to use language more geared towards the separate entity theory as most people who inquire about demons have some form of a theological paradigm or a belief in spirits. As an atheist mage discussing the same with other mages I discuss things in the terminology of the first theory outlined by Lud. Weirdly enough, my own paradigm shifts back and forth between the two rather readily.
Actually, I've expanded that original theory to account for that as well. I consider the Earth's magnetic field to be an emanation similar to the human aura, and like humans our world has its own "demons", its own nonphysical forces to accomplish its will. These forces would appear to us as anthropomorphic manifestations representative of the nature of its power. We call them elementals, djinn, angels, demons, and whatnot, but I'm fairly sure they're
of the same nature as our demons, if not the same source.