My personal understanding is that plants have a body, animals have both a body and a soul, and mankind has a body, a soul and a spirit. However, angels, as I understand, do not have a body that is physical. Jesus seems to have indicated this after His bodily resurrection.
See my hands and my feet, that it is I myself. Touch me, and see. For a spirit does not have flesh and bones as you see that I have. Luke 24:39 ESV
Are angels, then, classified as spirits, having no flesh and bones? If so, are they spirits with souls or just spirits?
I would like an answer from the perspective of those who hold to the tripartite nature of mankind (body, soul and spirit). I do not know if positions differ between the traditions of Protestant, Orthodox and Catholic. If they do, I am specifically interested in what Protestants believe on this issue and and in what ways this is distinct.