sewage smell?

How do I find where the sewage smell is coming from? I know it is around the toilet. We just purchased our house in May...the seller said that we have all new plumbing. The smell is kind of a mystery...it doesn't happen only when you flush, or run water, or take a shower. We can be asleep and it will wake me up, it smells so strong and bad. It just happens no particulair time or anything. It also smells outside sometimes. But there are no visable leaks outside. It does make the grout in our bathroom tile discolored. How do I know if it is just a toilet and something we might be able to repair or if it is something I will have to call a plumber in and pay thousands of dollars for.