The Torah uses the terms 'malak elohim' messenger of god, 'malak YHWH' messenger of the Lord, 'bene elohim' sons of God, and 'haqqodesim' the holy ones, to refer to beings traditionally interpreted as angels. The word angel is from the Greek for messenger.
Angels in the bible belong squarely in the prophetic tradition, in direct experience of revelation, communication with divinity through an intermediary being. The first person to refer to angels by specific names, is in The Book Of Daniel in what are clearly visions. In a modern, scientific sense, that would make them irrational.
“The angels are spirits. When they are simply spirits, they are not angels, but when they are sent, they become angels; for ‘angel’ is the name of a function not a nature. If you inquire about the nature of such beings, you find that they are spirits, if you ask what their office is, the answer is that they are angels. In respect of what they are, such creatures are spirits; in respect of what they do, they are angels. Make a comparison of human affairs. The name of someone’s nature is ‘human being,’ the name of his job is ‘soldier’” - Augustine, Exposition 1 of psalm 103,verse 4.
and, on when in Creation angels were made
For when God said, “Let there be light, and there was light,” if we are justified in understanding in this light the creation of the angels, then certainly they were created partakers of the eternal light which is the unchangeable Wisdom of God, by which all things were made, and whom we call the only-begotten Son of God; so that they, being illumined by the Light that created them, might themselves become light and be called “Day,” in participation of that unchangeable Light and Day which is the Word of God, by whom both themselves and all else were made." Augustine, City of God Book 11, Chapter 9
This approach seems to reconcile the many contrasting ways angels are pictured, from
"Forget not to show love unto strangers: for thereby some have entertained angels unawares." — Hebrews 13:2
"In appearance their form was human, but each of them had four faces and four wings. Their legs were straight; their feet were like those of a calf and gleamed like burnished bronze. Under their wings on their four sides they had human hands. All four of them had faces and wings, and the wings of one touched the wings of another. Each one went straight ahead; they did not turn as they moved.
Their faces looked like this: Each of the four had the face of a human being, and on the right side each had the face of a lion, and on the left the face of an ox; each also had the face of an eagle. Such were their faces. They each had two wings spreading out upward, each wing touching that of the creature on either side; and each had two other wings covering its body. Each one went straight ahead. Wherever the spirit would go, they would go, without turning as they went. The appearance of the living creatures was like burning coals of fire or like torches. Fire moved back and forth among the creatures; it was bright, and lightning flashed out of it. The creatures sped back and forth like flashes of lightning.
As I looked at the living creatures, I saw a wheel on the ground beside each creature with its four faces. This was the appearance and structure of the wheels: They sparkled like topaz, and all four looked alike. Each appeared to be made like a wheel intersecting a wheel." - Ezekiel 4-15
They seem to represent direct insight into the divine plan, or communication of it. In that sense, they represent contact with the deepest rationality.