I love the smell of hay, too. I've never really had a problem with rabbit poo smelling, but their urine definitely has a strong odor if the litterbox isn't cleaned often enough or if you're using a bad type of litter, let me tell you that! However, I never had a problem with Theodore (or his cage) smelling at all. In fact, none of my pets, past or present have as much of a problem with smell as my teddy bear hamster, Mowgli. He himself doesn't smell, but his URINE sure does. He always pees in the same corner, and I'm constantly cleaning it. It's a constant battle. You can't miss that smell. But our rabbits, cat, gerbils, birds, and rats never smelled, ever... even before the cage was cleaned.
I -have- smelled some stinky hutches, though... the wood really seeps up the urine odor. Yuck.