Irimi is off line. Sen sen no sen means you can't hit me. Sen no sen means you're too late. Any other thoughts means you have more to learn in my opinion.
Irimi as I have learned it is enter. Pure and simple. Enter. No specific path is implied other than that which allows me to control the center which varies a bit depending on situation. In eight basics as I was taught it sometimes it means directly entering ON centerline as for shomenuchi kokyunage, sometimes it means entering alongside as on tsuki kotegaishe. Where or from whom comes your belief it means off the line?