No locations in Oakland. Avis Locations at the San Francisco Airport and Oakland airports, as well as Berkeley. Avis has lots of other rental locations in the area, including Walnut Creek, downtown SF locations, and San Jose. Thrifty Locations at the San Francisco and Oakland airports, as well as downtown locations in both cities. Thrifty also has locations in Fremont, Hayward, and Richmond, but none in Berkeley.
Enterprise actually has tons of locations in the Bay Area in general.
National National doesn't provide an easy way to get location information, and their web site is currently down, so I'll update this information some time in the future.