There is absolutely such a thing as demonic terrorism and demonic obsession. Demonic terrorism is the sort of thing Job endured, Satanic forces caused physical harm to him and those around him. Demonic obsession is when a demon exerts influence, but not control, over a person's will; essentially, this is Satan trying to cajole a person into commiting sin. Unlike possession, demons do not need an invitation to engage in these two lessor forms of mischief.
Can true believers be possessed? I deffer to Scripture to tell me the answer is no. Can anyone produce a passage stating that believers cannot be possessed? If there is no such passage, then I would say that there is no such gaurenteed shield. I will, however, state that no demon can possess a person without the victim's permission. Free will is necessary to sin, thus a demon cannot control you unless you engage in a forbidden art- prophesying by false gods, fortune telling, necromancy, sorcery, drug abuse, channelling, or other forms of the occult. These arts are forbidden because they involve direct communion with demonic forces.