Demonic possession is not always the violent dramatic manifestations we are familiar with. It is as simple as any ground where satan has power, has one bound, oppressed or even one in his use building his kingdom of darkness. The most common is through sin, many people find them selves moved with powerful "feelings" and "emotions" that lead them into sin and they can not overcome...
It is possible to still obey Jesus while under this possession/oppression however it is MUCH more difficult, because the enemy is on the inside and not on the outside trying to work its way in. One of the biggest sins that lead people into possession is fornication..."
More on this: Many Are Possessed by Unclean Spirits