This was a former PE line; PE was absorbed into the SP in 1965. It survived long after passenger service ended in the 1950s because of some online freight shippers, mostly lumber yards and produce warehouses.
The entire abandoned segment ran in the median of Santa Monica Blvd., although there were several spurs that led to loading docks on either side of the street. The right-of-way was in a dirt median as far east as Croft Street. From that point further east, the rail were in pavement. According to the Pacific Railroad Society's Wheel Clicks newsletter, dated August 1973, the track extended as far east as Seward Street, which is where a lumber yard is located. (The segment beyond Seward Street had been abandoned in 1953.) Local freights ran at night, to minimize interference with cars and trucks on the street.
Thanks to Mike Palmer for contributing information about this route.