My research area has very few research positions, would it still be possible for me to stay in academia?
I wonder if it is still be possible for me to get a postdoc (possibly in one of the two places) and later go to a top-ranking school for tenure-track positions? 


Yes, this is possible. But, unless you are making definitive progress on famous open problems which are well-known to everyone in your field.... then it is very unlikely and you should not count on it. (And perhaps even if you are.)

Most academic jobs involve both research and teaching. For example, I work at a research university with a Ph.D. program and a 2-2 teaching load. I definitely have time for research, but teaching is a big component of the job, and if I didn't enjoy teaching I would not want to do this job. (Moreover, if I wasn't good at teaching, then the hiring committee probably would have picked up on this and not offered me the job in the first place. Most people who are good at teaching, enjoy it.)

I think you are wise to investigate your other options. I've known people who decided not to pursue (or continue with) academic careers, and for the most part they were able to find good jobs. Software companies like to hire mathematicians, and you might learn programming if you don't know it already. Some mathematicians successfully go into finance (and make boatloads of money doing it.) Actuarial work is another possibility. In any case, these sorts of jobs don't generally just "happen"; you have to proactively think about what you do like and look for opportunities.

Good luck to you!