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Which muscle of the human body is the strongest? Will I lose weight faster by focusing most of my training on developing this muscle?
The strongest muscle in the body is debatable. Some physiologists believe it's the masseter (used for chewing), while others claim it's the gluteus maximus (buttocks), or the rectus femoris (part of the quadriceps in the thigh). It's not easy to determine partly because muscles don't work alone. For example, you wouldn't be able to isolate the rectus femoris muscle and compare it directly to others because other quadriceps muscles contract along with it. There are biomechanical factors to consider as well like muscle length and the points on the bones where muscles attach called the origins and insertions.
What it sounds like you are getting at is the idea that if the strongest muscle in your body burns the most calories, then building it up would cause it to burn even more calories to help you lose weight. In pursuing this idea, I would go after the largest muscle in the body and not the strongest (particularly if it's the masseter), because surface area of the muscle has more impact on calorie expenditure than strength. What would be even better is to train a muscle that is both large and strong.
With this idea in mind, I suggest maximizing muscle surface area by building up the quadriceps and the gluteals (buttocks), two large and strong muscle groups. Train them with dynamic, multi-joint exercises like squats, leg presses, stair climbing, and lunges. Not only will these exercises help you develop your quads and glutes, but they also recruit muscles in the abdomen and back which will help you develop even more muscle and burn more calories.
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