Everything that God created is good, even the bodies and souls of those who damn themselves by choosing against Him. It seems that God would not annihilate something that is good in its essence: body and soul. Rather, since God is Justice, he will allow those who choose against Him to damn themselves, sentencing themselves to eternal punishment.
I agree with eternal punishment; annihilation is eternal punishment. Bodies, created good, are destroyed all the time; check out Hiroshima, highway of death, pictures from Rwanda, Sudan, Afghanistan, etc.
"Soul" as the bible defines it, it the combination of one's physical life and the body. Thus the Bible correctly speaks of "dead souls" and "destroying souls", that is to say, destroying life. Since Jesus speaks of God doing this in the judgment, this really isn't debatable.
The human spirit, our non-physical essence which gives us intellect (see 1 Corinthians 2), returns to God upon our death. (Ecclesiastes) It reunites with our body upon resurrection (see Jesus' resurrection of the Jarius' daughter; it says "her spirit returned to her".) God does not reveal what happens to the human spirit after the last judgment.
The soul is the form (in the classical Platonic/Aristotelian sense) of the body. Although every created thing has a form, the substantial form of man is unique. Since man can apprehend eternal things, his mind (soul) must be eternal.
I know there are references in the Bible to body, soul and spirit. I don't have an explanation for them. Perhaps spirit refers to the indwelling Spirit?
What verse and chapter of Ecclesiastes are you referring to?
The Jarius resurrection:
Luk 8:52 And all the people were weeping and crying for her; but he said, Do not be sad, for she is not dead, but sleeping.
Luk 8:53 And they were laughing at him, being certain that she was dead.
Luk 8:54 But he, taking her hand, said to her, My child, get up.
Luk 8:55 And her spirit came back to her and she got up straight away: and he gave orders that food was to be given to her.
In Luk 8:55, the Greek word translated "spirit" or "soul" in English is "pneuma". It can mean life, spirit, breathe, ghost or mind depending on the context it's used in.
It seems clear that in this context "spirit" means she returned to "life" or her "breath" returned. It's not clear that the author was saying that her "soul" departed from her, went to heaven, and then came back.