Legal Question in Landlord & Tenant Law in California

The 120 day rule means that after giving written notice that the property is for sale, they only need to give you verbal notice, not additional written notice, of intention to enter the property to show it for sales purposes for a period of 120 days. They still must give written notice of entry for other purposes except in emergencies. Notice also still has to be "reasonable" which is generally interpreted to be 24 hrs in most circumstances, and limited to "reasonable business hours" which is generally considered to be 9-5 or 9-6 weekdays and 10-4 or 10-5 Saturdays.

No you cannot refuse entry, unless you want to be in breach of your lease, and possibly incur liability for interference with contract (their listing contract with their agent/broker) and interference with prospective economic advantage (for interfering with their ability to sell the property). Considering most single family properties sell for more if they are vacant than if they have tenants, I'm sure the landlord would be happy to throw you out if you void your lease that way.

Ditto for removing the sign.