Could it be from Victoria, the Roman equivalent of the goddess Nike?
tl;dr - A late antique combination of Victoria and biblical tradition.
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.)
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. Yes, scholars pretty much agree that 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.
However, the theological reason is really twofold: on one hand, it's a useful shorthand to distinguish humans and angels in art; on the other, you have the powerful ideas of the winged cherubim and seraphim already out there.
Later developments will see the addition of childlike angels (today's "cherubs") and eunuch (standing in for asexual) characteristics to further distinguish angel and human in art, the "book of the illiterate."
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