There are two reasons for Satan to torment people: to keep them separated from God and to disrupt their witness of God. The second could be considered as being within the parameters of the first, except that the target of each is different. Satan's influence for the first is directed toward people who have not chosen God. The second is directed at Christians (those who have accepted Christ's gift of salvation).
Satan works often on the world stage to keep nonbelievers away from God. Unless an unbeliever is reaching a decision to accept Christ, Satan has no need to make any real effort toward them.
The Christian has accepted Christ's gift of salvation and becomes one of God's instruments to spread His word to others through witness of their belief in Christ and their relationship with Him. This makes the Christian a primary target for torment and temptation. Mark 4: 13 20 explains this Jesus own words.
The torment comes for the Christian if they give in to the temptation as it causes a chasm between the Christian and God. God says that he won't leave or forsake us. He keeps His promises, but we become tormented when Satan uses our emotion of guilt to cause us to feel inadequate to witness. He cannot take our souls back from God, but Satan can disrupt our testimony with falsehoods. Two references come to my mind for authority to say the above.
1. Romans 8 particularly verses 22 39
2. Psalms 103: 10 - 12
Satan is given many names in the Bible, first introduced in Genesis as the serpent.
Guilt is one of Satan's favorite torments of the Christian. God never causes us guilt, the perception than he does, is a misconception. What God does offer is to forgive and forget if we but repent. Repenting is a confession of the disobedience and a change so as not to repeat the same sin'. That doesn't mean that we won't, but God knows if we are not sincere.
There have been documented Biblical accounts of God punishing people for turning their backs on Him. Most of these are found in the Old Testament which is under the old covenant that God made with first Adam and later Moses to the Jews.
Adam and Eve were the first to give in to Satan's temptation and discover the torment of guilt and God's wrath. They tried to hide because they became aware of the presence and pleasure of giving into temptation. God did not turn His back on them, but He did send them out of the Garden of Eden and closed the gates behind them.
There are later examples including the example of Job where God knew the heart of Job. God knew the man would not turn his back on God. Satan challenged God, and God allowed Satan to plague Job. Job remained faithful and was rewarded for it.
That was one example of Satan inflicting physical and mental cruelty upon a man. But, these were directed at believers in God. Not at the nonbelievers. Job's witness to those around him was immense, because they marveled at his ability to remain faithful to a God who would allow these torments. The scripture of Job holds a full accounting of why and how this occurred, and needs to be read in context. However; Job 1:6 22 gives a good accounting of the meeting between God and Satan about Job's ability to remain faithful, and why the testing of Job was allowed.
After the death of Christ a new covenant was made with all men. Because Jesus paid the price of our sins forever, we only need to accept his gift and we are adopted children of God. John 3:16
This Satan hates. In fact he tried desperately to get Jesus to sin in order to disrupt his path toward being the only perfect human sacrifice. Jesus is God born in the flesh into the world. He is God the Father's Word, His promise of redemption.
A favorite torment of Satan on the Christian is to plant thoughts of doubt. Many Christians have placed a barrier between themselves and the Holy Spirit (God in Spirit that lives among and within us as a counselor).
Some of Satan's favorites are:
1. I'm not good enough to witness to others as a Christian.
2. If God so loves, how can he allow such pain in this world?
3. If I go out there and try to tell people about my Christian beliefs, they will ridicule me.
Satan does use the truth sometimes to slow down a Christian witness, as in number three above.
When a Christian witness is particularly strong, Satan will also use physical torment as noted by Paul in 2 Corinthians 12: 7 10. Paul suffered greatly for his faith and his witness; he was imprisoned and had skin disease. This is only one example of those who have suffered at the hands of non-Christians for their faithfulness. But, you do not see Paul bringing the glory to himself. He gives all glory, and rightly so, to God. In those cases Satan is thwarted.
The promise of our everlasting life in heaven is far more valuable to us than any torments we may suffer at the hands of Satan.