Is it permissible to accept a dinner invitation from a friend who is celebrating moving into a house he bought with usury?

It is not permissible to borrow with interest (riba) for building a residence unless there is an absolute necessity (ḍarūra) or an extreme need (ḥāja shadīda). If your friend is not in a state of necessity and bought a residence with usurious money, then you are not obliged to accept his invitation, and he must be advised to repent. However, if he was in a state of necessity, then there is no blame upon him for borrowing with interest to the extent of his need, and you may accept his invitation. Slaughtering an animal upon moving to a new home is permissible as a form of gratitude to Allah and to honor those who congratulate you. It is forbidden if it is done to ward off the evil eye or jinns, and it is major shirk (definition) (polytheism) if it is for the jinns.