How to make driving out demons reasonable for non-christians? Recently I invited some colleague students over to an evening called Questions to Christians at my student association. Two of them came (both almost) completely unfamiliar with Christianity/faith/God etc.) and we discussed several topics and read the story about the Good Samaritan. I gave both of them a copy of the New Testament and one said we would read the story of the Good Samaritan with our project group. Today one of them was browsing the bible and read some pages. He found the following sentence in Luke 11:14:


  Jesus was driving out a demon that was mute. [NIV]


He also found some other parts but this one made him laugh really hard. To quote: "Are you serious, you really believe this ****?" After this question I took the bible and imagined how it would be as non-Christian, unaware of a God/Devil/sin and could only come to the same reaction. Now I'm wondering, how can you explain such a text to a non-christian? In this case, how can you make driving out demons reasonable (acceptable) for non-Christians?

Note: This question may seem close to a pastoral advice question, however I'd say this question fits into this description in the FAQ: understanding the Bible from the perspective of a specific viewpoint.
There's a lot of baggage that comes with belief, but it's simple to explain:


God exists and he is pure spirit
God made Angels which are pure spirit

Some Angels are good
Some Angels are bad

God made the world
God made people with a body and a spirit


Humanity's ability to comprehend this ends at "people with a body".  Philosophers can come up with the rest without the assistance of revelation.  But all that is directly observable is that we exist because the rest is supernatural.  

As G.K. Chesterton wrote


  The strange truth about the matter is told in the very word "holiday." A bank holiday means presumably a day which bankers regard as holy. A half-holiday means, I suppose, a day on which a schoolboy is only partially holy. It is hard to see at first sight why so human a thing as leisure and larkiness should always have a religious origin. Rationally there appears no reason why we should not sing and give each other presents in honour of anything—the birth of Michael Angelo or the opening of Euston Station. But it does not work. As a fact, men only become greedily and gloriously material about something spiritualistic. Take away the Nicene Creed and similar things, and you do some strange wrong to the sellers of sausages. Take away the strange beauty of the saints, and what has remained to us is the far stranger ugliness of Wandsworth. Take away the supernatural, and what remains is the unnatural. 
  
  G.K. Chesterton - Heretics


So, when someone asks you if you "really believe all that stuff", ask them whether it's more likely that Santa Claus conquers mars or that St. Nicholas is a member of the Church Triumphant gloriously giving his intercession to all those who call upon him in the communion of saints. 



Specific to driving out demons.  Consider what it means, the mission of the Church and the Apostles was and is to go into places where people believed in demons, gave homage to them and worshiped them, and drive them out.  


  The new kingdom has an eminently spiritual character. To enter it, it is necessary to repent and believe in the Gospel, to be freed from the power of the spirit of darkness, to submit to the power of God's Spirit, which Christ brings to human beings. As Jesus says: "But if it is by the Spirit of God that I drive out demons, then the kingdom of God has come upon you" 
  
  Pope John Paul II - General Audience 11/4/1987


Whether or not the fellow you're in conversation believes in demons, he or she can certainly believe their absence is a good thing!  Maybe that's a place to start.