You are on a month-to-month lease. You have the right to end your lease with a month’s notice (sometimes less). You can exercise this right.
Or perhaps you want to stay or are asking about dealing with the owner marketing the property while you are still there.
I believe you have the right to 24-hour notice for showings. You do not have to leave the premises during the showings. See the reference belowfor more details …
If I were you, I would make lemonade out of the situation, even profit from it. Ask them to credit you some amount off the rent (e.g. $300 per month) in exchange for the hassle of say a 2-hour or 4-hour notice to show. Since you are living there, do not consent to lock boxes. It depends on your tolerance for trading off dollars for hassle and the owner’s willingness to negotiate this item, but take it under consideration.
Or if the whole process is too invasive, simply insist on your right to 24-hour notice and give your notice to vacate under the terms of your loan.