Angels are not necessarily holy nor unholy. The word angel in the Bible comes from the Hebrew word “mal’ak” or the Greek word “aggelos,” both meaning “messenger.” Angel can refer to human messengers such as in Matthew 11:7-10 which quotes Malachi 3:1, “…I will send my messenger [angel] ahead of you, who will prepare your way before you.” In this instance angel refers to John the Baptist. The word angel, however, is often interpreted as a spirit being, which could be holy or unholy. Some well known angels are Gabriel, Michael, and Lucifer.
In the Bible, Holy is the Hebrew word “Qodesh” or the Greek word “Hagios.” Old Testament usage of the word holy may be applied to things. For example, the Tabernacle and its furnishings were holy: “the holy altar” (Ex 29:37), “the holy anointing oil” (Ex 30:25), “the holy high priest's garments” (Ex 31:10), etc. In other contexts, holy describes “the holy sabbath day of rest” (Ex 35:2). Holy may also be applied to people, such as in 1 Peter 1:15-16 which quotes Leviticus 11:44-45, “You also be holy in all your conduct.”
A practical definition of holy is something that is set aside; special; for God; dedicated to God. God himself is Holy (Leviticus 11:44-45).
Thus, angels that are set aside to do God’s work would be considered holy (Matthew 25:31), such as Gabriel or Michael. Others, however, such as Satan (Lucifer) and the fallen angels (Jude 1:6, 2 Peter 2:4), would be considered unholy.