If the smell is inside the car all the time, it's probably oil dripping onto the crossover pipe like turbolou said, just look under the car on the exhaust pipe that goes across the car under the oil pan and see if there is a big wet oil spot on it,if there is then your valve cover gaskets are leaking and the oil is running down onto the pipe(Very Common).
If you are outside the car and getting a strong dirty smelling exhaust then it's because your cat is gutted,(Once the cat is removed they always smell like dirty exhaust, but not always inside the car when driving, but if your oil is leaking onto the crossover you will get that smell inside and outside of the car.
You probably have a combination of both.
Without the cat it's going to stink and you will definetly need one for a cal sticker anyway,so thats's a definite need to fix item and should clear up a good part of the smell too.
Welcome to the world of the turbo buick.