There are many problems with what your priest is supposedly saying. But it is apparent why you believe the way you do.
You (and your priest) had better review the Catechism of the Catholic Church on its fundamental doctrine on Original Sin, (#413-421 summary) There are NO EXCEPTIONS save one: The Immaculate Conception.
This INFALLIBLE Doctrine of the Catholic Church in no way contradicts the passages you have quoted, yet you ignore the Gospel of John 3:13. Your interpretation of the passages you quoted is reading into them what is not there, but imposing a Fundamentalist Christian (not Catholic) view upon them.
Saying Enoch, Elijah, Moses, and whoever else you might think of, all avoided death and were assumed directly into heaven, DOES VIOLENCE to Catholic Church doctrine on Original Sin, and the Redemption of Jesus Christ. These are ALL infallible doctrines that REQUIRE faith of Catholics. It also DOES VIOLENCE to the extraordinary significance of the Immaculate Conception and Assumption of our Blessed Mother.
Even the Eastern Church doctrine holds to our “fallen nature” after the fall of Adam and Eve, and therefore required Redemption by Jesus Christ the Messiah BEFORE anyone could enter Heaven.
Here’s a great link for you and your priest:
Enoch, Elijah and Moses -Not a Catholic website, but still has very good answers for you BASED ON SCRIPTURE