Did you both move into the same house? In that case the house is singular.
"Her and my" or "our" are possessive adjectives. Either expression would be grammatically correct. As a matter of usage, if Sue is your wife, for example, then it would be usual to say "our". If Sue is merely an acquaintance, and each of you part owns the house, then "her and my" could be used, to indicate that you are two separate individuals who happen to co-own a house, rather than an item.
Did she move into her house and you move into yours? In that case there is more than one house and so you should say "houses". in that case the usual expression would be to say: "Sue and I moved into our respective houses".