Ed Sheeran songs fall under the Category of Folk Rock, Acoustic, hip-hop and grime.
Folk Rock combines elements of Folk music and Rock music, Acoustic music means that the music is created through entirely acoustic instruments, no electric instruments are used.
The hip-hop elements of his music is seen only in the tempo or some general melodys, not in his style or lyrics. The grime elements in his music are apparent through the small use of electrically made instruments.
The characteristics mainly used for his songs are narrative based storys, they include him or others going around to different places perhaps meeting up with people and generally showing an everyday life. This is typical of folk rock or acoustic genre music videos.