You are clearly a very strong and very competitive applicant.
MIT and Harvard and Stanford do not admit by major. I think that the same is true at Caltech. Being Asian will not help, but being exceptional will help. I think that is it worth applications but your chances are not very far off from the admissions rate – perhaps slightly higher for some and slightly lower for some (eg MIT does not consider legacy and does not have much in the way of athletic admissions, whereas Stanford does consider legacy and does have many athletic admissions).
You should either make sure your parents are okay with full pay (>$300,000 for four years) or run the NPCs and make sure that your parents are okay with the cost. Expect UC Berkeley to be full cost if you are admitted.
Definitely apply to Ohio State given that it is a great university and you are in-state. You could do very well with a degree from Ohio State. A bachelor’s degree from OSU plus a master’s from one of the top ranked universities is a very good option to consider.
You chances would be much higher at the top Canadian universities (Toronto, McGill) than the top US universities both because they have more slots per population and because being Asian will not hurt you nearly as much in Canada. However, in your situation I might tend to stick with OSU if you do not get into a top US university for undergrad.
I think that you are going to do well wherever you go to university. I specifically think that you will do well if you do end up at OSU for your first (bachelor’s) degree.
Then run the NPCs. There is not much point in looking at three or four acceptances to top schools that you cannot afford, plus an acceptance to OSU. You might as well keep it simple and just get the acceptance to OSU.