Wild Mass Guessing for The One I Love Is...:
Shinji did not go in detail about those days, but it is likely the three of them had many emotionally-charged talks in which they tried to reconnect again. And it would not be weird at some point Asuka pitied Rei, said she could share their bedding space for the old days' sake... and in one of those nights as they were reaching each other out, talking about their feelings, and sobbing their hearts out, one thing led to another and they had sex because Asuka refused to share Shinji's heart but she and Shinji wanted to lessen Rei's pain and loneliness.
Whether it was an one-night-stand or they slept together more times throughout the years and they never told anybody it is a different matter of speculation.