There is a basement to the home I just rented. My landlords initially told me they would be removing all of their storage items and then renigged. They come over at all times without notice and enter the basement for access to their storage meanwhile, mine is unsecured. All agreements were oral, month to month lease.
Your landlord cannot come in to your house whenever they choose its against the law. They generally need to give you 24 hours notice unless it is some type of emergency. However if you are on a month to month lease and not under rent control they could terminate your lease if you complain on 30 to 60 days notice.
So I would suggest that you get a lease in writing for a longer period of time if you want to continue to live there then tell them to stay out of your house.
Good luck and hope that helps.
Melvin C. Belli
The Belli Law Firm
35 Miller Ave Suite 199
Mill Valley, CA 94941