What is the ruling on my remaining in my husband's house, as he claims to have divorced me twice, while I am certain that he divorced me three times, knowing that I am pregnant?

If you are certain that your husband has divorced you with a triple divorce, then you must strive to free yourself from him (khul') with whatever means you can. It is not permissible for you to willingly allow him access to yourself. It is permissible for you to flee from his house, and you must refuse and escape from him. You should free yourself from him (khul') with whatever you are capable of. It is not lawful for you to marry another man before obtaining khul' from him or a judicial ruling of divorce, because you are, apparently, still under his marital authority. This is with the caveat that scholars differ on the occurrence of divorce in some cases, but the fatwa issued is that it does occur.