In a nutshell, my husband is not a Calvinist in any way, shape or form. He doesn't subscribe to the TULIP, doesn't believe in imputed righteousness, nor the Calvinist rendering of predestination.
In the conversation with my priest, my husband was bending over backwards to explain what he meant by old nature. He redefined the term in several ways, i.e.: passions, the flesh, old man, etc. With that said, I realize that it isn't natures that sin per se, but persons.
Honestly, I think my husband (I'll include myself here too) is just trying to get a grasp on the following from an Orthodox perspective:
1. What does it mean to be human and how is our humanness/humanity effected by the indwelling of the Holy Spirit?
2. How is the battle against the passions of the flesh waged and how are we victorious in this battle?.
3. What role does the mind play in this ascetic struggle?
4. What role does the heart play in this ascetic struggle?
5. What role does the will play in this ascetic struggle?
6. How does one know if they are living according to the flesh?
7. How does one know if they are living according to the spirit?
8. How does one gauge whether or not they are making progress or failing in the ascetic struggle?
9. What role does the Church play in helping us to succeed in the ascetic struggle?
I'm sure I have more questions but these are good for a start.
I am tempted to simply answer "yes" to all of your questions.
Question #1 is an interesting question. #2-#7 can only be answered by a life of prayer and ascetical struggle. All other answers are silly. #8 is easy: the sacramental and ascetical life of the Church.