John 4:24 (KJV) God is a Spirit: and they that worship him must worship him in spirit and in truth.
The Gospel of John tells us that God is a Spirit. What about the angels? According to the Bible, what are angels? Are they also spirits or something else?
When Abraham's servant went to find a wife for Isaac (Gen 24), he had angelic influence (no mention of the angel physically accompanying him). The angels who came to escort Lot and his family out of town were corporeal as they ate dinner (Gen 19:3). In Matthew 2:13, an angel appears to Joseph in a dream. However, an angel was able to physically kick Peter in the side to wake him up (Acts 12:7). The author of Hebrews says we may entertain angels (13:2) which suggests a physical form.
It would seem angels have the ability to assume both corporeal and non corporeal forms as they see fit, suggesting they have both physical and spirit attributes.
From the Cathecism of the Catholic Church:
CCC 328 The existence of the spiritual, non-corporeal beings that Sacred Scripture usually calls "angels" is a truth of faith. The witness of Scripture is as clear as the unanimity of Tradition.
CCC 329 St. Augustine says: "'Angel' is the name of their office, not of their nature. If you seek the name of their nature, it is 'spirit'; if you seek the name of their office, it is 'angel': from what they are, 'spirit', from what they do, 'angel.'" With their whole beings the angels are servants and messengers of God. Because they "always behold the face of my Father who is in heaven" they are the "mighty ones who do his word, hearkening to the voice of his word".
CCC 330 As purely spiritual creatures angels have intelligence and will: they are personal and immortal creatures, surpassing in perfection all visible creatures, as the splendor of their glory bears witness.
It should be noted that the ability for people to interact and see angels constitutes a miracle. Being a miracle, one cannot produce conclusions of the angelic nature from such events.
