Make website full responsive by using javascript
No, this is not the "normal" way to build a responsive website. "Normally" people use frameworks that are built specifically to remedy this problem.

Bootstrap, made by the guys who run Twitter, is the most popular responsive framework. Basically it's a set of styles and (opionally) javascript that you include in your sites and then you just add class names to your HTML depending on how you want things arranged. It's really easy to learn and use. Much easier than writing 1000s of lines of JS or CSS.