Legally does the sheriffs department in California have jurisdiction in the entire county?

Depends on the county in question. Here in L.A. County a lot of independent cities contract with the Sheriff's Dept. so you could have one of those that's completely surrounded by another city, Los Angeles for instance. But here the LAPD and the LASD work well together so there aren't a lot of disputes about the overlap. But much of this state is pretty rural and in those places your County Sheriff's Dept. would likely have a lot more authority over those living in small towns in the deserts and mountains.

The County the Dept.  has Jurisdiction over; yes.  Not All counties, no.  This includes and cities that might "surround " it. 

In EVERY jurisdiction where there IS a COUNTY Sheriff, their jurisdiction MUST BE the entire county.

The sheriff's department is the primary law enforcer for the entire county. They still have jurisdiction even if the city has their own department.

I don't know California law, but they probably do in every state that has counties and sheriffs. (Louisiana has parishes instead of counties. )

Only in their own county/jurisdiction...