Why do so many oil paintings show cherubim with only heads and wings and no bodies?

You are not looking at the most common lower order of angels, but at the upper three levels of the Cherubim, the wise angels, the higher angels, along with the fiery seraphim,

Repeatedly referred to in different chapters of the Bible, with varying descriptions, but generally described as winged celestial beings who are both human and animal and who are subservient to God. The three orders and nine classes of angels are often very different from what we think of, and if you are interested, you can search for pictures of them, and they are also found in many paintings in Europe.

Today cherubim and angels in general are sometimes recognized as synonymous.