What Happens After Death?

Souls die: Eternal death, yes. Do you believe that this death of soul equates to a ceasing-to-be?

I think we're using different terminology. The Hebrew word most commonly translated as "soul" in the OT is "nephesh":

nephesh
From H5314; properly a breathing creature, that is, animal or (abstractly) vitality; used very widely in a literal, accommodated or figurative sense (bodily or mental): - any, appetite, beast, body, breath, creature, X dead (-ly), desire, X [dis-] contented, X fish, ghost, + greedy, he, heart (-y), (hath, X jeopardy of) life (X in jeopardy), lust, man, me, mind, mortality, one, own, person, pleasure, (her-, him-, my-, thy-) self, them (your) -selves, + slay, soul, + tablet, they, thing, (X she) will, X would have it.

"Soul" is simply a term for something that has life. It can be an animal or a human. When something lacks life, it lacks soul. The life, the soul, is non-existent. The body and soul are dead.

Therefore, to say that Christ was subject to death just as we sinners are is to posit that Christ was a sinner, which clearly is not the case.

He wasn't subject to death...being sinless. That's what makes his murder/crucifixion all the more heinous. This is how he paid the entire price for mankind.....one and for all. He was innocent!

You're stating something I already believe.

"Soul" is simply a term for something that has life. It can be an animal or a human. When something lacks life, it lacks soul. The life, the soul, is non-existent. The body and soul are dead.

In what way would you distinguish between animal soul and human soul, and in what sense do you believe that man was created "in the image and likeness of God"?

In what way would you distinguish between animal soul and human soul,

Again, the term "soul" as used in scripture basically means a breathing creature, whether human or animal. For example:

Gen 1:20 And God said, Let the waters bring forth abundantly the moving creature (nephesh) that hath life, and fowl that may fly above the earth in the open firmament of heaven.

Gen 1:21 And God created great whales, and every living creature (nephesh) that moveth, which the waters brought forth abundantly, after their kind, and every winged fowl after his kind: and God saw that it was good.

Gen 1:24 And God said, Let the earth bring forth the living creature (nephesh) after his kind, cattle, and creeping thing, and beast of the earth after his kind: and it was so.

In each one of the verses above (and many others I won't bother to list) the hebrew word "nephesh" is used. This is the exact same word used here:

Gen 2:7 And the LORD God formed man of the dust of the ground, and breathed into his nostrils the breath of life; and man became a living soul.(nephesh)

Animals ARE a soul, and humans ARE a soul. At least according to the bible.

and in what sense do you believe that man was created "in the image and likeness of God"?

In many ways. But I suspect that you're really asking for the difference between man and animal. The difference is that man was created with a spirit, which is an image of (but IS not) God's spirit. The spirit of man is a non-physical component of who we are and is what gives us the power of rational thought, intellect...our "mind". Our spirit is NOT eternal, it is something that is created by God:

Zec 12:1 The burden of the word of the LORD concerning Israel. Thus declares the LORD who stretches out the heavens, lays the foundation of the earth, and forms the spirit of man within him,

Without our spirit, we cannot think and are not conscious:

Psa 104:29 You hide Your face, they are dismayed; You take away their spirit, they expire And return to their dust.

Psa 146:4 His spirit departs, he returns to the earth; In that very day his thoughts perish.

Our spirit joins with the spirit of God, the holy spirit, when we begin our Christian walk:

Rom 8:16 The Spirit itself beareth witness with our spirit, that we are the children of God:

More scripture concerining the spirit of man. Here Paul contrasts how mans spirit allows us to know and understand the things of man (something animals don't have the capability of doing) with how God's spirit allows us to know and understand the things of God:

1Co 2:11 For what man knoweth the things of a man, save the spirit of man which is in him? even so the things of God knoweth no man, but the Spirit of God.
1Co 2:12 Now we have received, not the spirit of the world, but the Spirit which is of God; that we might know the things that are freely given to us of God.