In order to apply for a job (such as Post-Doc, tenure track, visiting,
instructorship,...) in U.S., you need to have the following items
prepared and upload them in mathjob.org (by AMS)

1. Research statement
2. CV
3. Teaching statement
4. AMS cover sheet
5. cover letter
6. (At least) 4 reference letters
7. Publication list

However, the last item may not be mandatory for some universities.
It is necessary that one of the reference letters address your
teaching skill and experience, except when you apply for some research
institutes. In some cases, you might need more letters.
If you have any connection with professors in U.S., that should
be better than asking professors for letters from outside.
Try to get to know someone who can judge and understand your research.

In my personal opinion, it'd be better to start your graduate school
overseas rather than deciding to leave after becoming a Post-Doc, since
the only difficulty is the lack of some proper evaluations of your
teaching skill in English, or some other languages. This is quite
typical in U.S., leaving out some exceptional people.

But, there is no way out if you do not try. NEVER GIVE UP!!!