Where does the belief that we will be given immortal bodies on the day of resurrection come from.?

That's true.  When God sentenced Adam and Eve to die and cast them out of the garden, it was to deny them access to the tree of life.

And the Lord God said, “The man has now become like one of us, knowing good and evil. He must not be allowed to reach out his hand and take also from the tree of life and eat, and live forever.” So the Lord God banished him from the Garden of Eden to work the ground from which he had been taken.  After he drove the man out, he placed on the east side of the Garden of Eden cherubim and a flaming sword flashing back and forth to guard the way to the tree of life.

Even immortal bodies require divine sustenance.

Revelation says there will be a new heaven and Earth and will we live there. I take this to mean we will have immortal bodies like Jesus. 

It's scripture Gloria - it's from God's pure Word, the Bible.  Only those who are in the FIRST resurrection are blessed and holy because over those, the second death has no power (Revelation 20: 5 & 6).

When Jesus returns with the spirits of those already dead in Christ, who He said He would bring with Him when He returns (1 Thessalonians 4:14) "He shall descend from heaven with a shout with the voice of the archangel and the trump of God, and the DEAD IN CHRIST SHALL RISE FIRST" -  (that's the FIRST resurrection of those already dead in Christ whose bodies are in the grave but whose spirits are with Christ coming back with Him as above because they are saved.) - "then we who are alive and remain, shall be caught up together with them in the clouds to meet the Lord in the air and thus we shall ever be with the Lord. (1 Thessalonians 4:16).

When this FIRST resurrection occurs, the dead and the alive in Christ - as we rise together to meet the Lord in the clouds, in the air, (1 Thessalonians 4:16) -  "we shall all be changed, in a moment in the twinkling of an eye at the last trump.  For the trumpet will sound and the dead will be raised INCORRUPTIBLE and we shall be changed.  For this corruption must put on INCORRUPTION and this mortal must put on IMMORTALITY, and when that happens this saying shall be brought to pass that is written,

"O death where is thy sting? O Hades (or grave) where is your victory* (1 Corinthians 15: 50 - 55)

Were Adam and Eve created with immortal bodies? No, but their perfect earthly bodies provided by God could exist forever as long as they obeyed God. So their bodies COULD exist forever but were not immortal. Same with Christians who hope to live on the earth forever. - Ge 2:17, 3:18; Psalm 37:29; 1 Cor 15:47-48.

Only Christians who rule with Christ from heaven  receive immortal spirit bodies. Immortals in the Bible: Jehovah God, Jesus and the 144,000 after being resurrected. - 1 Cor 15:50-55; 1 Tim 1:17; 6:15-16.

There is no scripture that says we receive immortality when resurrected in the future on the earth, once resurrected if you obey the rules given to us, and pass the final test you will be given EVERLASTING life.

There is a difference between (everlasting and immortality) everlasting life is forever as long as you do not sin like Adam & Eve did, immortality is forever, you can never die.

Where does the belief that we will be given immortal bodies, it comes from false religion

All religions are based on GUESSES and FEELINGS.

When Jesus died for our sin on the ten foot cross nine feet cross him came back to lif and walked among us

The Bible.

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We are told that our physical bodies will be like Jesus' resurrected body.  It seems that you don't understand that Revelation is symbolism, neighbor.  Jesus is the "tree of life", it's not a literal tree.