In short no: the other spirits do not possess nor give powers to people.
Spirits: Angels or Demons
Angels = of God
Demons = not of God
Hebrew 1:14 "Are they not the angels all ministering spirits, sent forth to minister for them who shall be heirs of salvation?"
Matthew 4:11 "Then the devil leaveth him, and, behold, angels came and ministered unto him."
Luke 22:43 "And there appeared an angel unto him from heaven, strengthening him."
If angels can minister to the heirs of salvation, then likewise, demons can as well but they minister for Satan's cause not God's.
2 Corinthians 11:13 For such are false apostles, deceitful workers, transforming themselves into the apostles of Christ. And no marvel; for Satan himself is transformed into an angel of light. Therefore it is no great thing if his ministers also be transformed as the ministers of righteousness; whose end shall be according to their works.
So we must try the spirits, knowing whether they are of God--teaching and preaching God's word, or if they come appearing as minister's of righteousness but teach and preach Satanic doctrine.