The list of nine choirs of angels goes back to the fourth century A.D. The 2007 edition of The Catholic Source Book (Harcourt Brace) identifies these choirs in ascending order as angels (many references in the Old Testament and New Testament), archangels (Jude 6:9 and 1 Thessalonians 4:16), principalities (Romans 8:38 and Colossians 1:16), powers (same references), virtues, dominations (Colossians 1:16), thrones (Colossians 1:16), cherubim (plural of cherub, Genesis 3:24, Exodus 25:18) and seraphim (plural of seraph, Isaiah 6:7).
See http://en.wikipedia.org/wiki/Christian_angelic_hierarchy for a short description of the duties of the various choirs of angels.
Although no Scripture text confirms this, my guess is that Satan belonged to the seraphim (those closest to God) but lost that position through his pride and disobedience. Non-scriptural texts suggest that Satan was originally among the highest of the angels.
In his Letter to the Colossians, St. Paul warned the Christians there against trying to enlist angels to guarantee a particular outcome of events. Because angels are diversified signs of God’s providence, they are never a means of manipulating God for our advantage.
Cardinal William Levada, prefect of the Congregation for the Doctrine of the Faith, wrote to the world’s bishops last October, cautioning them about a splinter group from the Church-approved Opus Angelorum (“work of angels”) group. The dissenters refuse to accept corrections of certain beliefs and liturgical practices linked to private revelations to Gabrielle Bitterlich in 1946.
In sections 328 through 336, the Catechism of the Catholic Church emphasizes that angels are God’s servants and messengers, reminding us of the “blessed company” we are intended to share with them. The Catechism does not list the choirs of angels, their duties, number or creation.