Is it permissible to live in a house bought with haram money for the purpose of marriage, given the inability to purchase a dwelling with halal money?

If the illicit money with which you bought the house was usurped or stolen from a specific person, then it must be returned to him or to his heirs. If that is not possible, then donate it on his behalf. However, if you acquired the illicit money through your own effort or through a usurious loan which you then repaid, then there is no harm in you owning the house. You must repent and seek forgiveness.