How long does the pill birth control wear off ?

Within a week or two I think

The hormones are only active in your body for a little over 24 hours -- that's why it has to be taken daily to be effective. 
When you stop, you will have some withdrawal bleeding. Some people will have their first "normal" period right on schedule a month later. Others may have either a prolonged period of spotting first, or no bleeding at all for a few months. 
Most people will be back on their regular cycle in 2 or 3 months at the most.