Hola Ashlyn, 

Época can be used instead of período but not usually tiempo, though the teachers may know when tiempo would work. I think of tiempo as being used when thinking about time as a concept, or in general terms, like "The first time I ate callos (tripe) was unforgettable." I don't recommend it by the way.

I think of época and período as meaning a period in time or an era. For example: "The 60's was an [época / período / era] of experimentation in fashion and music." I think época is more formal than período or era, but I have used it a lot and it seems to be acceptable.

I hope that helps. Saludos. John