I will answer your question by referring you to two books, but with this proviso (not to argue, just so as you know where I stand.) A person is either anointed with God's Holy Spirit, or they are not. All Christians are anointed with God's Holy Spirit (Romans 8:1-17). The matter of efficacy in casting out demons has to do with two things in particular, as my quotes from those books should show - the afflicted person honestly answering the Christian's questions as to the sources of their having become possessed, and the persistence of the Christian in not letting the demonic powers get away with their powerful resistance.
The two books which provide first-hand instruction in the matter of casting out demons are autobiographies of a lady who was so possessed, for many years, until she got help from a Christian. They are her personal experience. They are not text-books on "How to Cast out Demons". They are not theology books on "What Does the Bible Say about Casting out Demons?"
First, I quote from From Witchcraft to Christ by Doreen Irvine. She descended to the depths of being lover of the Chief Satanist in Britain, and becoming Queen of Black Witches for a year. These quotes deal with her gradual deliverance from demons via a Rev. Arthur Neil who began the process, continued over many sessions:
P154 "I became aware, suddenly, of the evil spirits within me. They
actually possessed my body. The evil spirits spoke again, but only to
me. “Tell him nothing, nothing.”
Now, I was no stranger to demons. Had I not often called on them to
assist me in rites as witch and Satanist? For the first time I knew
these demons were within me, not outside. It was a startling
revelation. But I said nothing, nothing about witchcraft or Satanism,
or anything at all.
There was no need, for Mr. Neil knew I was demon-possessed, if he knew
nothing else about me. He pointed his finger at me – yet not at me
myself but at the demons within. He spoke in a strange tongue that the
demons understood, commanding them to leave in the name of Jesus. I
sat terrified in the chair… Mr. Neil knew that a long and deep
ministry with me had only just begun…
P155 I had the most dreadful night. In the early hours of the morning
I awoke filled with the most awful fear. I was surrounded by evil
powers. I heard the awful voices, but this time they gave their names.
I was torn inside as if someone had taken a knife and was tearing me
to pieces. Tossing back and forth as the demons within tormented and
tore me, I heard this:
“Have nothing to do with Neil. I am Doubt and Unbelief. I am not
Then many more voices cried out all at once: “Not me! Not me! Not me!”
It sounded like a mighty chorus growing louder and louder. I was
perspiring, the bed clothes were soaking wet, my body was torn by the
I heard again another voice say, “I am Lust. I am an unclean spirit. I
am not leaving. I have been here for years.” “I am Lies,” said
another. “I’m not leaving either”. “And I am Witchcraft,” said
another very powerful demon.” “I am Pride,” said another. “I am not
leaving.” “No, nor I.” “Nor I.”…
P159 The exorcism lasted three or four hours. In this time the demon
Deceit and the unclean spirits of Lust, Lies, Pride, and Witchcraft
were despatched to Gehenna.
The demon of Witchcraft, said Mr. Neil, was very noisy. Its nature was
weird and gave expression by certain enchanted wailings. “Do you know
the witch of Endor?” It almost sang in weird, bewitching tones. “It
tried to bewitch me,” Mr. Neil told me, “but I resisted it in the
authority of the name of Jesus Christ, consigning it to Gehenna.”
“Not there, not there!” wailed the Witchcraft spirit. “I must have her
body. I will not leave her body. I need a body. Not there! Not there!
“You will not possess her body or any other body,” said Mr. Neil. “I
command you to leave her body and go now to Gehenna, in the name of
Jesus Christ.” But the Witchcraft demon was very obstinate. The
exchanges went on for some time before Mr. Neil with a final word of
command opened the nearby door and commanded the spirit to leave and
go straight to Gehenna. It did – with terrific screams and wailings,
saying: “All right, all right. I’m going.”
I fell to the floor as if dead, said Mr. Neil. …My throat was bruised,
and so were my ribs and my arms. But the six demons were gone. Mr.
Neil prayed for me… That night I slept like a baby." From Witchcraft
to Christ, Doreen Irvine, David Cook originally 1973, this edition
There were many more demons that were also cast out. In her second book, Set Free to Serve Christ, Doreen detailed her ministry as a Christian, and she helped others to be delivered from their demon-possession.
Page 83 "Judy was a bright and attractive student with a wonderful
future before her. However, her fellow students persuaded her to go
and see a hypnotist, somehow believing that he could see her through
her final exams with flying colours. They had apparently been to him
themselves. Three or four days after visiting the hypnotist, Judy
became severely depressed and would burst into tears at the slightest
provocation. Within a few short weeks she had changed from a normally
happy girl into a sullen, withdrawn, bad-tempered and irritable
person. Her ability to concentrate had vanished completely and she
became irrational and in every way unreliable. Suddenly she had become
the exact opposite of her true self...
P85 About this time she came along to one of my meetings and stayed
behind to speak to me. It was very difficult to talk to her as she was
scarcely able to concentrate enough to explain her problem. I knew
that Satan was robbing her of thoughts and did not want me to discover
the root cause of her troubles. Judy was utterly confused and very
frightened. I rebuked the Devil and the power of darkness in the name
of Jesus and asked the Lord to show me what was wrong. I paused for a
few moments, then I asked her if she had been in contact with a
fortune-teller, medium or hypnotist. As soon as I mentioned the word
‘hypnotist’ she became hysterical and began to sob and shake from head
to foot. The presence of evil was obvious and it was with great
difficulty that I kept her from rushing out of the room and into the
night. Laying my hands om her head I again rebuked the forces of
darkness and she slowly calmed down and was then able to tell me of
her visit to the hypnotist and how she had been affected by it.
It was plain to me that Judy was being oppressed heavily by the same
evil influence that controlled the hypnotist. In the name of Jesus I
commanded every demonic power to depart and never to return, and they
did so immediately. Judy had been set free. The evil atmosphere that
had filled the room was dissipated and the peace and presence of Jesus
could be felt in a very real way. Judy’s face changed from fear to
relief and joy. She later told me that if something had not been done
that day, she would probably have tried to commit suicide! ...she
passed her final exams with flying colours." Set Free to Serve
Christ, Doreen Irvine, Nova Publishing, 1979. This 3rd printing 1989.
Another account in this second book by Doreen shows how her dealings with others required them to repent of particular sins before they could be set fully free from the power of evil. So, it may be that some success gained in exorcism is lost due to the person not repenting, and so demonic powers get back in. This would not be the 'fault' of any Christian having 'insufficient' anointing of the Holy Spirit.
After this long answer, my short answer is that efficacy in casting out demons is not down to one single 'thing', but is a complex matter, though nobody lacking the anointing of the Holy Spirit could cast our demons at all, to any degree - Mark 3:22-30.