God created multitudes of angels, including at least three archangels: Lucifer, Michael and Gabriel. Angels are spirit beings which may or may not manifest themselves in a visible form (usually not). All angels were created good and holy but Lucifer, the chief worship angel decided to exalt himself and led a rebellion in heaven against God.
Ezek. 28:13-15 "Thou hast been in Eden the garden of God; every precious stone [was] thy covering, the sardius, topaz, and the diamond, the beryl, the onyx, and the jasper, the sapphire, the emerald, and the carbuncle, and gold: the workmanship of thy tabrets and of thy pipes was prepared in thee in the day that thou wast created. Thou [art] the anointed cherub that covereth; and I have set thee [so]: thou wast upon the holy mountain of God; thou hast walked up and down in the midst of the stones of fire. Thou [wast] perfect in thy ways from the day that thou wast created, till iniquity was found in thee."
Is 14:12-15 "How art thou fallen from heaven, O Lucifer, son of the morning! [how] art thou cut down to the ground, which didst weaken the nations! For thou hast said in thine heart, I will ascend into heaven, I will exalt my throne above the stars of God: I will sit also upon the mount of the congregation, in the sides of the north: I will ascend above the heights of the clouds; I will be like the most High. Yet thou shalt be brought down to hell, to the sides of the pit."
Lucifer and his angels were cast out of heaven and became Satan and his evil spirits.
2 Peter 2:4 "For if God spared not the angels that sinned, but cast [them] down to hell, and delivered [them] into chains of darkness, to be reserved unto judgment;"
Satan is active today in the air and in the earth.
Job 1:7 "And the LORD said unto Satan, Whence comest thou? Then Satan answered the LORD, and said, From going to and fro in the earth, and from walking up and down in it."
Eph 2:2 "Wherein in time past ye walked according to the course of this world, according to the prince of the power of the air, the spirit that now worketh in the children of disobedience:"
Not being everywhere at once, as God is, he works through his forces, including fallen angels and demons. These spirits seek to live in and work through people, usually in a hidden way - usually not openly. The results of Satans work are still evident in our world today. Jesus came to destroy these works.
1 John 3:8 "He that committeth sin is of the devil; for the devil sinneth from the beginning. For this purpose the Son of God was manifested, that he might destroy the works of the devil."
Now, Are Demons Fallen Angels? The bible is not perfectly clear on this, but it serves logic to assume that as Lucifer is Satan, so are the Fallen Angels, his minions.
In every Christian resiedes the Holy Spirit. It is not possible for a Christian to be possessed by any other spirit than God.