Could you tell me what happens if you start birth control pills mid-cycle, during or right after ovulation?

You can start anytim: You are likely to get more irregular bleeding in the first month of taking the pills, if you start mid-cycle, and (of course) you are not protected during the period you describe (b/c if you ovulated, then there is an egg available to be fertilized, so you need the back up method for the first month after starting the pill). Regardless of when you start taking it.