This sounds like a definite new-territory struggle for you and your cat. Where do you have his/her litter box at and does (i'm going to call it a she because I've always had she cats) she know where it is located? It is most likely that the cat is still adjusting to the new territory, although I'm not for certain as I'm not a vet and I haven't moved any pets.
I suggest to ease some stress try calling a vet and asking (even the secretary) some information on your cat's irregular bowel movement. it could very well be that there are scents of other pets still in the house that your cat is picking up, and you know how animals act upon territory.
If you end up taking the cat to the vet, I suggest borrowing a kennel carrier as that cat will be much more easier to handle taking into the vet clinic. if you can borrow one from someone you can even save some money or just check around. I'm not too sure on the cost, but if you have to buy one you can always use it later on.
Try dropping your cat in her litter box a few times throughout the next few days, to be SURE the cat knows where the litter box is, maybe even keep it in a more open spot depending on how big the house is.
I hope you enjoy your new place, is it a big house with a nice neighborhood? You'll most likely be introduced by your neighbors eventually and things will start to calm down. Even strange noises... every house makes them, you'll soon be accustomed to it, just be rational with what it could be and hell go and check it out just to push past the fear.