Translation:The workers save the fish from the oil.
If you mean "saving the files" like computer files that you save before exiting an application you would use "Jag sparar filerna." Jag räddar filerna would either mean that you were to rescue some files off a corrupt hard drive. "I am saving the files" could also mean "Jag räddar akterna" where it would refer to saving files of an archive from fire or something else.
That's not the point, is it? The beauty of this sentence is that the translation is far from obvious by context - so it exercises your true understanding. I'm all in favour of this approach. Can anyone from DL tell us whether some of these examples are picked randomly from newspapers etc? If so, that's a great idea!