Do angels have wings?

They do not have wings. Being energy, they are non-physical, so this is non-sensical. There is a historical view of them in that aspect, but it is a metaphorical representation that they are from a higher plane and that is represented nicely through the imagery of giving them wings with which to fly. The idea of them flying down from heaven to assist and then returning bird-like is a way for primitive people to conceptualize how a divine agent might enter their realm to carry out a duty, but then be gone once again. The people down through ancient times have not been able to conceive of actions taking place via consciousness alone, but this is often how angelics carry out their duties—impinging on human beings as well as things in the environment through the effect of their consciousness, to impinge on the target, and make a change or adjustment in the energies accordingly, as may be needed to solve a problem or bring requested support. This is why so many divine interventions happen on a routine basis but go unnoticed. They are simply invisible in their mechanism of action and this is because the angelics are invisible. They are depicted in a simplistic fashion, but that is in keeping with the limited knowledge and awareness in prior eras, and even to this day there is but a poor understanding of energy and the role of consciousness in making things happen. It will be some time yet before humans have broad awareness of how things really work, let alone a true understanding of what is taking place.