ANSWER: The Bible does clearly state that evil demonic powers do exist. The fifth chapter of Mark records the incredible miracle of Jesus casting out a group of spirits who had possessed a man. These demonic powers were able to give the person they possessed super-human power, such as the ability to break any chain or shackle put on them. Jesus met this man, who lived in a graveyard, right after he got off a boat on Lake Galilee.
Nobody could keep him tied with chains any more (the man had MANY demonic spirits in him!); many times his feet and his hands had been tied, but every time he broke the chains and smashed the irons on his feet. He was too strong for anyone to control him (Mark 5:3 - 4)
Demons are real! People become possessed, many times, by such disobedient spirits because of some bitterness or resentment THEY hold against God about something. Until they repent of their rotten attitudes, they will continue to have such difficulties with demons. Jesus warns us in the Sermon on the Mount (Matthew 5) that we need to forgive and love everyone.
In the book of Matthew chapter 12 Christ revealed He cast out evil beings by the power of God's Holy Spirit (Matthew 12:28). He told the self-righteous religious leaders, who criticized and hated him, that it did not make any sense that one demonic being would use or give their powers to cast out another one from someone. Jesus then asked them a very pointed question they were too embarrassed to answer!
Well, then, who gives YOUR followers (the Pharisees had their sons and others they trained) the power to drive them out? (Matthew 12:27)
The implication Jesus is making here (which most people miss) is that the Pharisees nor their sons or even their students could cast out rebellious spirits from people! Yet, somehow, they feel they can rightly condemn Jesus for doing what they would love to do but cannot (See also Acts 19:13 - 17)!
In Matthew 10 Jesus gave His disciples the authority to cast out fallen angels from people as well as heal them (Matthew 10:5, 7 - 8). In Mark 9, the apostle John said a man was casting out evil spirits by using Christ's name (or by Christ's authority). Jesus' quick answer was that the person should not stop from casting out demons. He also added, in this case, that someone who is able to do this using his (Jesus') name would not be someone who would be against him (Mark 9:38 - 40).
When confronted by strange happenings or evil spirits at home, put these scriptures together, start to pray and ask God to rebuke them in the name of Jesus Christ. You should continue to pray until the disobedient spirits leave. At times, such unwelcome guests in a house or other places are NOT there because of you, but because of some previous demented person.
If your house experienced these strange events before you moved in, then it is very likely they came to your house by someone in the past before you lived there. Either way, you and your family can pray to God to rid you of these beings by Christ's authority or in his name. If this does not stop the problem, your family should consider moving rather than dealing with such disobedient spirits.