Seems to me that an immortal is a mortal(human being) who can never die, whether we are talking about the physical body and/or the soul. So the Saints could be considered to be immortal by the grace of God. However, it doesn't seem right to claim Jesus is immortal since he was never a mortal(human being). Jesus had a human nature, but remained Divine in "person" and in 'being". That being said, it seems that only the term Eternal can apply to Jesus since Jesus had no beginning, has no end, and was never a mortal.
The Divine Mercy prayer calls God by the term "Holy Immortal One",... Sister Faustina from my understanding received that prayer from Jesus himself when he appeared to her.
Also, from my understanding, before Vatican II the Divine Mercy apparition occurrence was being condemned by the Church, but later was revived by John Paul II.
So, what are your thoughts on this?