While I was researching body, soul, and spirit in Scripture, I found that were are no verses in Scripture explicity referring to an "eternal body", an "eternal soul", or an "eternal spirit" with one exception: Hebrews 9:14 refers to the eternal Spirit of G-d (through which Messiah offered Himself).
As mentioned earlier, Paul writes of an imperishable body raised at the resurrection of the dead (1 Corinthians 15:34-50) but we have no answer about whether or not that body is of the same type of flesh as our current bodies. It is of greater glory, true, but is it fundamentally different in some measurable, quantifiable way? Many think that it is while others focus on verse 44 where Paul makes a distinction between a "natural body" and a "spiritual body".
This is uncertain.
Some verses may imply an eternal spirit:
Furthermore, men are afraid of a high place and of terrors on the road; the almond tree blossoms, the grasshopper drags himself along, and the caperberry is ineffective. For man goes to his eternal home while mourners go about in the street. Remember Him before the silver cord is broken and the golden bowl is crushed, the pitcher by the well is shattered and the wheel at the cistern is crushed; then the dust will return to the earth as it was, and the spirit will return to G-d who gave it. (Ecclesiastes 12:5-7)
This seems to indicate that when "man goes to his eternal home" it is his spirit that will return to G-d. This spirit appears to be given some type of new container/body as described in Paul's second letter to the congregation at Corinth:
For we know that if the earthly tent which is our house is torn down, we have a building from G-d, a house not made with hands, eternal in the heavens. For indeed in this house we groan, longing to be clothed with our dwelling from heaven, inasmuch as we, having put it on, will not be found naked. For indeed while we are in this tent, we groan, being burdened, because we do not want to be unclothed but to be clothed, so that what is mortal will be swallowed up by life. Now He who prepared us for this very purpose is G-d, who gave to us the Spirit as a pledge. Therefore, being always of good courage, and knowing that while we are at home in the body we are absent from the Lord-- for we walk by faith, not by sight-- we are of good courage, I say, and prefer rather to be absent from the body and to be at home with the Lord. (2 Corinthians 5:1-8)
Although eternal bodies, souls, and spirits (for humans) aren't explicity mentioned, there is one thing that is found: references to eternal life. In fact, eternal life is mentioned 43 times in the Greek Scriptures.
In Matthew 19:16 the Master was asked "What must I do to inherit eternal life"? His response? "Keep the commandments." Please note that it is not the keeping of the commandments that provides eternal life (as shown in verse 21). Following the commandments is evidence of eternal life and a love for G-d ("If you love Me, you will keep My commandments" - John 14:15). The faith given to us as a gift (Ephesians 2:8) brings us into a state of spiritual rebirth in a relationship with Messiah, being known by Him (Matthew 7:23), and being among those whom He has chosen (2 Thessalonians 2:13). This is how we are saved: it is G-d's work and not ours.
When Messiah answered this way, He was responding to the question in a very Hebraic way. It is very similar to His answer to John's disciples in Matthew 11:4-6: look at what I do to determine who I am.
John 3:36 also provides some clarity on this point:
"He who believes in the Son has eternal life; but he who does not obey the Son will not see life, but the wrath of G-d abides on him." (John 3:36)
If we tie together the concept of "eternal life" with the declaration from Scripture that "life is in the blood" this suggests having an "eternal body" which contains the blood in which is eternal life. This is conjecture but it definitely makes for some interesting discussion.
While I was searching Scripture for the words "eternal" and "spirit", the word "forever" cropped up instead of "eternal" and it pointed to this fascinating passage from Isaiah:
"A Redeemer will come to Zion, And to those who turn from transgression [literally: willful sin] in Jacob," declares the LORD. "As for Me, this is My covenant with them," says the LORD: "My Spirit which is upon you, and My words which I have put in your mouth shall not depart from your mouth, nor from the mouth of your offspring, nor from the mouth of your offspring's offspring," says the LORD, "from now and forever." (Isaiah 59:20-21)
Isaiah tells us that the Redeemer will come to those who turn from willful sin and the Spirit which is upon them and the Word of G-d that is in their mouth shall not depart from their mouth... forever. What a wonderful promise!
Body, soul, spirit, and life. These are all intertwining concepts of our existence in this world and the world to come.
Now to the King eternal, immortal, invisible, the only God, be honor and glory forever and ever. Amen. (1 Timothy 1:17)