There seems to be no Garden of Eden, no Original Sin, and no Fall of Man in the legendarium. There are the Undying Lands of Valinor, the Kinslayings by Elves of Elves, and the Gift of Men. Obviously, these do not map onto Old Testament theology as the legendarium is not allegory by design.
Tolkien set out to create a montheistic mythology for the English that substituted angels (Valar) for Anglo-Saxon deities, but not a thinly disguised version of Abrahamic beliefs. As he stated later, he realised that his Catholic beliefs diffused into it although that was not his original intention.
I have no real idea of the nature of sin and good and evil in the legendarium - other than it seems Eru appears to be instantiating the struggle within His own consciousness as a physically manifested world where his thoughts can contest with each other. There is perhaps more pantheism, Taoism, or elements of the Mandukya Upanishad than Abrahamic monotheism in this interpretation.
That's my interpretation anyway. Anyone honed in theology will probably disagree and offer valid arguments as to why I'm oversimplifying and way off the mark.