My brother is joint-tenancy owner of my father's house. My father has passed away and we now want to rent or sell the house. Do we have to give notice to our step-mother to vacate? If so, how much notice? The house is in California.

... Do we have to give notice to our step-mother to vacate? If so, how much notice? The house is in California.

Yes you do.

She would have a tenancy at will, so the required notice would be 30 days.

CA Codes (civ:789-793) (http://www.leginfo.ca.gov/cgi-bin/displaycode?section=civ&group=00001-01000&file=789-793)

If she's been living there longer than 2 years then the required notice would be 60 days.

Also has the home cleared probate, and has she contested the will in any way.

If the property was owned by the father and brother as joint tenants then probate and a will shouldn't matter.