You have hit on one of the main differences between the Old Testament view and the New testament view. Intresting to look these terms up in a scolarly bible dictionary. "Soul" in the hebrew refered to physical things, ie desire, hunger for food, long earthly life,etc. In the Greek "soul" referred to more spiritual things even including the statement that body and soul are not the same and are killed seperatly. Understanding that Jesus was dealing with only the Old testament or old Jewish belief system where "perfection in the flesh" was the pursuit and the soul "nepish" died with the body, his new view that the soul "psyche" did not die with the body, was not yet being taught, puts a new light on things. The JW's ofcorse want to oversimplify the whole Bible and would have us believe that the words translated from Hebrew and from Greek mean the same thing, but in fact the Jews before Jesus time had a little different feeling as to just what the "soul" was then did the Christians after Jesus time.
Did Jesus have a soul as describbed in the New Testament? If so it left his body at death where he voluntered to stay in Hell for 3 days, then it rose to heaven. Trying to combine the Jewish view and the Christian one, the Catholics have indicated that "some" a very few of the saints have been raised with thier physical bodies which have dissapeared or ascended into heaven. No other explanition is offered that I have found, it is one of those things that you must take on faith if you would choose to believe it.