Is it permissible to reside in a house bought by the non-Muslim parents of the wife with an interest-based loan from the bank, knowing that they did so to help the couple, and is there sin upon them for that?

The prohibition in usurious loans pertains to the borrower's liability, not to the specific loan itself. Therefore, there is no harm in residing in the house that the wife's parents bought with a usurious loan, and there is no sin upon the resident. The couple is advised to invite the wife's parents to Islam and seek assistance from callers to faith.