If a contractor was supposed to build my house and has already been paid, but quit working on it when it was only halfway built, what can I do?

This is a serious legal matter.  Generally, contractors are paid in step payments as the progress takes place.  Here, it sounds that you paid the contractor in advance.   You need to find a local attorney who will file a lawsuit against this contractor.  Not only are out the money you paid the contractor for the incomplete job, but you are now paying expenses for living expenses elsewhere, plus the emotional distress this has caused you.  You need to take legal action as soon as possible.  You are on the side of the angels, not the contractor.