If you want to quickly gain a substantial amount of ELO abusing OP champions is the only way. You can slowly learn and improve your play by focusing on the basics such as CS skills and map awareness, as well as improving your ability with the selection of champions you enjoy. That is a way to improve your skill, and in turn ELO, but it is in no way fast. OP is looking for a fast way, and that is what he's getting from us.
Also, don't make a mistake. I personally put playing champions I enjoy ahead of the OP ones, I don't even actually own any commonly recognized as OP. I don't even play all that much, and as a result I constantly hover between 1250 and 1350, not above average at all.
It's just that I'm not above giving advice contrary to my personal beliefs if it is objectively sound.