News flash: The majority of Asian men look like "twinks;" it's our body type, not a disease that needs to be cured. Who's embracing an ecto frame? I'm lifting, losing weight, and getting into shape. I feel better than I have in years. My feet don't hurt from carrying excess weight. I don't feel sluggish throughout the day and my energy levels are getting higher. Even if I wanted to move bigass weight, I can't. Years of wrestling and judo jacked up my wrists, knees, and shoulders. When doing squats with just the bar, I can't get my quads parallel with the ground without my knees hurting. I can't deadlift 155 lbs. without my wrist popping out on me and hurting for weeks afterwards. My body has its limitations due to genetics and the stress I put on it throughout the years, but I'm working with it the best I can.
Now if your goal is to lift heavy weights, that's cool with me. Maybe you can have some respect for someone with different fitness goals.
Just FYI, the ecto/meso/endo thing has generally been discredited:
http://en.wikipedia.org/wiki/Somatotype_and_constitutional_psychology
As for being Asian, well, I have lived, worked and gone to gyms in Asia for the last 13 years, and I have seen plenty of big Asian guys. At least from the waist up- people here seem to skip leg day a lot, just like everyone else.
If you have a less muscular frame than others, it's probably not because you are Asian or because you are an "Ectomorph". It is probably just because over the course of your life you ate comparatively little and you did relatively little of the kinds of exercise that promote muscular growth.
That being said, why do you care why you have comparatively little muscle? If you don't want it, and you think your body can't handle the work needed to acquire it, that's all that really matters. The reason you ended up with the frame you have is just a theoretical question.
Anyway, the reason for lifting heavy weights for an athlete is usually to increase power/explosiveness. Actually gaining muscle usually isn't too desirable because of weight classes or ideal proportions and weights for certain types of sports. We tend to give people a hard time because a lot of people who turn up here are delusional about their weight and body composition- "I am 6"1 and 160lbs, with a muscular frame, and I am looking at cutting" sort of thing. So for quite a few people who turn up here lifting weights is an important part of recomposition/moving towards more optimal size, weight etc.
All these things being said, I will try to answer your question:
Stronglifts isn't going to be a great programme for you because it is meant to be done progressively (adding 5/10lbs a time). It will take you above the level where you are experiencing pain. To get really strong, you would need to progress quite far beyond that level for some time, and that's evidently not really practical.
As for being "functional" or not, people here don't like the term because it is associated with people doing incline dumbbell bench press with 2lb dumbbells on Bosu balls. And also it's used as a term to make out that real strength training doesn't have any part in athletic development. There is a legitimate concept in there, though- it's the concept of being able to execute the movements of your sport (or profession or whatever) with great force or power. And as far as that goes.. it's possible to execute movements with force or power without lifting weights, it's just that most people will be able to execute them even more strongly or powerfully with some correctly applied strength training. But stronglifts capped at a 150lb deadlift will probably not make any difference.
As for being "toned", well, it will probably increase your muscle tone (passive muscular activation) and capped at those weights you are not going to get much bigger if at all. So who knows, maybe you will achieve your desired aesthetic. Although probably pretty much any reasonably vigorous physical activity will have more or less the same results.
Personally, if I was in your situation, though, I would focus on doing what I had to do to be able to lift properly again. I don't know what you have been though, but there are people on this board who have come back from multiple very serious injuries, sometimes requiring years of recovery, so hopefully it would be possible. Then you can lift properly, and get strong. If you don't want to get bigger, you just don't eat a calorie surplus.