The power to cast out demons comes either from God or from Satan, it cannot be both.
It is possible to cast out demons by Satanic power, exorcism is a good example. They exercise that power in league with, or as agents of Satan, “the prince of the devils, Matthew 12:24. The Pharisees accused Jesus of casting out demons by the power of Satan while actually they themselves were the servants of Satan, seeking to frustrate the work of God.
What did Jesus use to cast out devils?
He casted out devils only with the finger of God; He said, “But if I with the finger of God cast out devils, no doubt the kingdom of God is come upon you, Luke 11:20.
What is the finger of God?
The Spirit of God is, for he said in Matthew 12:28, “But if I cast out devils by the Spirit of God, then the kingdom of God is come unto you.”
How did Jesus cast out devils?
“And Jesus rebuked the devil; and he departed out of him: and the child was cured from that very hour.” Matthew 17:18
Jesus would only rebuke devils.
“And he shewed me Joshua the high priest standing before the angel of the Lord, and Satan standing at his right hand to resist him. And the Lord said unto Satan, The Lord rebuke thee, O Satan; even the Lord that hath chosen Jerusalem rebuke thee: is not this a brand plucked out of the fire?” Zechariah 3:1-2
Wherever or whenever the devil shows up, rebuke him.
“Yet Michael the archangel, when contending with the devil he disputed about the body of Moses, durst not bring against him a railing accusation, but said, The Lord rebuke thee.” Jude 1:9
To rebuke is to express sharp disapproval or criticism of someone because of their behaviour or actions. The devil takes in rebuke, reproof and will bow down when resisted. “Resist the devil, and he will flee from you,” James 4:7. No need to bring against him railing accusations, or name calling. Where you do, you risk corrupting yourself. Remember, “…the weapons of our warfare are not carnal, but mighty through God to the pulling down of strong holds; Casting down imaginations, and every high thing that exalteth itself against the knowledge of God, and bringing into captivity every thought to the obedience of Christ.” 2 Corinthians 10:4-5
Who else can cast out devils?
Obviously every believer, including yourself.
“And he said unto them, Go ye into all the world, and preach the gospel to every creature. He that believeth and is baptized shall be saved; but he that believeth not shall be damned. And these signs shall follow them that believe; In my name shall they cast out devils; they shall speak with new tongues.” Mark 16:15-17
Using the same finger of God, you also can cast out devils, from day one you got saved. “And they overcame him [satan] by the blood of the Lamb, and by the word of their testimony; and they loved not their lives unto the death.” Revelation 12:1.
The finger of God to you is the name Jesus Christ, is the blood of Jesus and of course the Spirit of Christ in you. Jesus is happy for you to use that name. Actually he’s instructed that you do – forbid him not, “And John answered and said, Master, we saw one casting out devils in thy name; and we forbad him, because he followeth not with us. And Jesus said unto him, Forbid him not: for he that is not against us is for us.” Luke 9:49-50