First, I actually don't know much about Jewish depictions of angels, and whether they're the same as Christian depictions.
But anyway. We're all familiar with angels depicted as slightly androgynous men with wings. And a man with multiple wings is mentioned, like, once or twice in the Bible, but in metaphorical sections (Revelation, etc). But mostly the New Testament, especially in the sections intended to be read as "this is what happened" not "this is a metaphorical vision I had" (such as the Gospels) depict them as young men. The Old Testament mainly seems to just say "Angels" with no description at all ("I saw the Angel of the Lord," "Abraham was visited by some angels"). And then you get stuff where people have visions of angels as wheels covered in eyes, beasts with 4 faces and 6 wings, etc.
So where did these winged men come from, that are so common in art? Greece? (I assume the winged babies are from Greece). Zorastrianism? What?
I have some earlier answers on angel iconography! Here's one I really like that discusses the Eldritch Abomination/humans with wings issue:
The Bible bequeaths two basic traditions of angels and what they look like: "basically men" (e.g. Mark 16:5, Gen 18), and grotesqueries with wings. As Ezekiel 1 describes the cherubim, "In appearance their form was human, but each of them had four faces and four wings... 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." The seraphim of Isaiah 6 have six wings and are covered in eyes, even under their wings!
The acid trip angel type pretty clearly comes out of ancient Near Eastern traditions--both the etymological roots of cherub and seraph and artistic depictions track back to Phoenician, Assyrian, Hittite art. (The Jewish Encyclopedia offers some nice illustrations.)
Strictly speaking, in the Hebrew Bible the cherubim and seraphim are not "angels" as such--angels were more strictly limited to "messengers of God" whereas the C&S are kind of "flyer-praisers of God." However, almost from the beginning of serious Christian theology, the category "angel" has been flattened out into generic non-human celestial creature. (That early date probably means it has roots in apocalyptic Judaism). Late antique and medieval Christian theologians used, as one method, a form of biblical interpretation called allegory, in which Bible stories, teachings, people, &c. actually stand in for a second, deeper meaning (relating to Christ, to morality, or to eschatology and the Last Things). Origen, Eusebius, & Co. all have different allegorical interpretations of the seraphim in Isaiah--but they all agree that the creatures are prophets--hence, angels. Furthermore, the theologians tag specifically the wings of the seraphim as signifying divine communication.
As for the human appearance angels, in the earliest Christian art they do not have wings! It is only after the conversion of Constantine and the full incorporation of Christianity into the Roman Empire that we have traces of that tradition. Scholars pretty much agree that Nike/Victoria is the iconographic or artistic model for humanform angels' acquisition of wings (Keck, Angels and Angelology in the Middle Ages does a good rundown of the bibliography on this, going back to 1898!). This parallels a contemporary adoption of other Greco-Roman artistic traditions into Christian art. It seems likely that the wings of the seraphim and cherubim, now understood as angels, influenced the choice of Nike as a model.
This medieval painting, of St. Francis of Assisi receiving the stigmata, shows how neatly artists could link the six-winged seraph with a more winged-human, less eldritch image. Given this particular scene, the seraph's somewhat flame-like appearance is also no accident. Not only are angels traditionally associated with fire and light, but the scene in the Legenda major of Francis being depicted is stocked full with fire imagery.
Later developments will see the addition of childlike angels (today's "cherubs") and eunuch (standing in for unsexed) characteristics to further distinguish angel and human in art /u/caffarelli has a post talking about eunuchs and angels, too, if you're interested!
Art was the "book of the illiterate," and make no mistake, it held and holds probably the most powerful sway over our conception of angels. Let me tell you about this theologian not named Dionysius. Yes, we know so very little absolutely nothing about him, not even his real name (in Acts of the Apostles, a judge named Dionysius and a woman named Damaris convert to Christianity on the steps of the Areopagus; our theologian adopts the name to give themself greater authority by picking a male biblical figure). And yet, Pseudo-Dionysius, as they are known today, manages to be this MASSIVELY important player in the development of Christian theology and, well, language: they literally invent the word "hierarchy."
More specifically, they invent the word hierarchy to describe first of all the ranking orders of angels! Incidentally, not only does Pseuds have the seraphim and cherubim as angels in the generic sense (there are also Angels, proper), but they are the highest two orders of angel. Relevant to present purposes, however, Pseuds spends a good bit of On the Celestial Hierarchy talking about all the different appearances angels are said to take:
Chapter 15: What are the formed images of the angelic powers? The fiery property, the human likeness, the eyes, the nostrils, the ears, mouth, sense of touch, eyelids, eyebrows, fingers, teeth, shoulders, elbows and hands, heart, chest, back, feet, wings, nakedness, garments, the bright clothing, the clerical clothing, the belts, the sceptres, the spears, axes, plumb lines, winds, clouds, brass, electron, choirs, clapping, colors of different stones, the likeness of the lion, of the ox, of the eagle, the horses, the differences in the horses' colors, the rivers, chariots, wheels
(trans. Colm Luibheid)
I remind you: this is the theologian who (a) invented the idea of a hierarchy of angels (b) invented the word hierarchy to describe them (c) was influential enough that we know Angels, Archangels, Cherubim, Seraphim, etc are all forms of "angel" (d) was influential enough that we use the word hierarchy at all. And they think angels can have the formed images according to all those appearances. And say so in this same text!
...But you don't think of angels as different colored horses and as wearing priests' vestments and as freaking wheels, do you? No, you think of Hallmark cherubs, or of the pity part they give all the other girls in Sunday school Nativity plays.
Not to discourage further answers but /u/sunagainstgold discusses some of your questions here: https://www.reddit.com/r/AskHistorians/comments/i2k2cp/whenhow_did_the_image_for_angels_in_christianity/g0605vg/?utm_source=reddit&utm_medium=web2x&context=3
