Jesus needed to teach the disciples about the most important reality of Satan's authority - it is limited, and easily overpowered by God.  Exposing the illogicality of the Jews' assertion that He had cast out demons by the devil's permission (Luke 11:15-20), He used the simple example of household security guards.  If they are stronger than would-be robbers, then the house is safe.  But if somebody with superior strength comes, the house is vulnerable to whatever the stronger man wants to do.

This analogy unusually describes Jesus as the strong man who is ready to break into Satan's house (Luke 4:34).  That is just what Jesus did when He cast out demons.  He was invading Satan's self-proclaimed territory and demonstrated that Satan's power was useless against His Word of command.  This is why the demons were forced to leave the poor individuals they had been terrorising.  

So, far from using Satan's power in such miracles, Jesus was overpowering the devil and taking control of his evil servants - thus showing Satan to be conquerable.  There was only one authority that could defeat the prince of darkness - God Himself (Luke 11:20).  When Jesus described Himself as the Light of the World (John 8:12), He was claiming Divinity: when Jesus cast out demons, He was proving it.

It should be a huge relief to Christians, that our spiritual enemy is not all-powerful.  Jesus, our Saviour, has proved that the darkness of evil cannot swallow up God's people.  Instead, the Lord has given Satan 'notice to quit' and one day will eliminate his power totally (Revelation 20:10).  Until then, nothing, including demons, can separate us from God's love (Romans 8:38-39), and the devil cannot win against God's purposes (as the resurrection demonstrated).  So, if you are trusting in Jesus, rejoice! "... the One who is in you is greater than the one who is in the world." (1 John 4:4). Therefore, do not let yourself be intimidated by Satan's threats, or allow yourself to believe that Jesus is not Lord of all.  Furthermore, in the Name of Jesus, demons must go.  Trusting in Jesus is not just a nice idea; there is real power in His Name - so do not fear anyone.