In the youth lesson for 5/6/2015, we studied a pericope (passage of scripture) about Jesus encountering and healing a demon possessed man. This isn't too controversial necessarily, but when dealing with beings as fantastical and unrelatable as demons, it can sometimes help to dig a little deeper.
Many people think of demons as fallen angels...servants of God who revolted against their heavenly creator and were thus cast down out of heaven as punishment. The problem, is that those definitions cannot really be found in the Bible. In fact, if angels had free will to rebel against God, it may require us to reconsider what exactly was special about man being "made in God's image". Essentially every Bible text dealing with demons is found in the New Testament, and when Jesus or his disciples encounter them, they are generally an "evil spirit", or unseen force, which is causing a problem for a person. It is not unreasonable, nor is it corrosive to the witness of scripture, to consider these "demons" as mental illnesses.
While Jesus was God and thus all-knowing, he time and again interacted with people in a way they could understand. He spoke in folksy parables, explained away his resurrections (Matthew 9:18 & 24), and healed people in ways common to the times (John 9:6...saliva was thought to have special or magic properties in ancient times). One might say that Jesus didn't want to blow peoples minds...too much. He met them in their own context.
There is nothing wrong with believing in demons in a traditional sense, but do not let their mention cause you to doubt scripture. The world is more rationally understood now than it was when the books of the Bible were being written. If Christ would have waited until today to come, would it be less a miracle if he healed a paranoid-schizophrenic or split-personality sufferer by simply talking to them? Of course not.
It is not specific terms and ethereal beings that give the Bible it's credence, but rather the timelessness of God's love towards, self-revelation to, and reclamation of mankind.