Well, I would use 'on' in both of those sentences. There's a post office on West Street. It's on Market Street.

This is a hard question because you DO hear both being used. I think saying "There's a post office on West Street" is grammatically correct. From how I see it, using "IN" is to refer to something being "inside". For example, "There is chocolate in my milk." Another example is a street where I live, it's called "China Town". Because the street is narrow and somewhat enclosed, people say, "There is a nice noodle shop in China Town". I guess the only explanation I can provide is, think of whether you are physically walking INTO something. It won't work for all cases, but most.

We can use either 'on' or 'in' in British English. Both seem natural, and the 'on' version doesn't sound noticeably American to us.

Thank you very much, Adrian.

I think your suggestion is correct, but 'on' is often used in British English as well, particularly in reference to locations on main [major] roads [as opposed to side streets].