WHAT DOES A DEMON ACTUALLY "POSSESS," THE BODY OR THE SOUL?

It is a common misconception that demons possess souls.  They do not.  The soul and its two spiritual faculties of mind and will are closed realms to the devil, and he cannot penetrate them.  Demons strickly speaking, "possess" only bodies.  Demons can exercise a certain measure of control over mind and will, however.  They can so "override" these faculties as to cause the person to lose both consciousness and freedom, sometimes completely, but this does not mean that they possess these faculties.  They remain uniquely the property of their human owner, which is why it is possible for a person in a totally possessed state to remain without sin. There is always some realm of the person that the devil is not permitted access to.

What is most common, however, is the evil's penetration of the emotional and sensitive parts of the human soul, traditionally known as the memory or imagination.  This is the realm of images, senses, passions and memories to which the devil can have access because they are more tied to the flesh than the other spiritual faculties of mind and will.   The devil can attack and manipulate these sensitive parts of the human soul with experiences of severe nightmares, voices, unclean images, visions, etc.  This is usually why people who are possessed or seriously obesessed suffer so much.  They are attacked in the sensitive parts of the soul.

By. Fr. Thomas Euteneuer "Exorcism And The Church Militant" pg 41.