Just to share my experience so far. I am starting to hesitate that some relaxation exercise will "cure" the eye strain issue for me.
I am training with Alexander Technique and Feldenkrais for the last 3 years, i may even become a teacher in one if these techniques sometime in the near future, just to demonstrate my level of involvement. It all started as a way to help me with back pain. I am an chartered accountant by profession and long sitting hours had an impact on my back.
In the above techniques we work a lot with the releasing extra tension in the eyes, in the jaw as well the neck. The techniques had such a profound effect on me that even my issue with chronic blocked sinuses have started to feel a lot better without medication. My neck, jaw and eyes are way more "relaxed" or released than 3 years ago. My sleep quality is very good, no teeth clenching or anything like that.
Actually I am 40 and in combination with jogging (3 days per week 30 min per session), i am in the best bodily state ever. I do not follow a special diet though, i am just careful not to eat junk.
However the strain issue, while there is some improvement, is still there. I can actually feel my eyes relaxed and very easy to move but when i sit in front of a newer laptop my eyes become tense and i get an intense headache and neck cramps.