Let's say if one starts a good, systematical strength training programme at the age of 30. I would say he should be physically much stronger when he turns 40. What if he just continue this training programme? Can his strength just continue to grow, despite the aging? Or in other words, can he be physically stronger when he is 70, or 80 years old, compared with when he was 30 or 40?
This depends on what you mean by "physically stronger". There are a few ways of interpreting this question.
Is it possible for me to lift heavier weights at 80 than I did at 40?
Yes. If you'd never trained a day in your life before 40, and you suddenly started working out, AND barring any other physical illness (this is the real caveat), then it is entirely possible. In fact, the physical training could help you prevent certain physical illnesses.
Is it possible for me to prevent the effects of aging and entropy by working out?
No. Not with our current scientific knowledge.
One clue should be world records in different lifts, and at what age they are set, I'll take the "worlds strongest man" competition as a basis for my calculation of "strongest" age.
2014 - Žydrūnas Savickas - 38 years
2009 - Žydrūnas Savickas - 33 years
2004 - Vasyl Virastyuk - 30 years
1999 - Jouko Ahola - 29
1989 - Jamie Reeves - 27
1979 - Don Reinhoudt - 34
Those are just some random picks, but the average age of these is: 32 years old.
So with optimal training, you will peak around 30-35 years old. However, if you start weight lifting at 30, it's pretty clear that you will peak later, and so on.
A lot of old people get extra testosterone to counter the falling levels these days because it seems to be healthy, so I guess you could prolong your golden days a bit unless you're competing.