What I do is this- I put paint thinner in a dispenser with a very small hole- and shove it as close or inside the cable as possible and squeeze the dispenser.
Then I'd wait for a minute then use my air compressor to force the thinner through. After it runs out the other end along with the rust and old grease- I then try moving the cable like Joew said. After it has moved some, then load the other end with wd40 to clean out the paint thinner and blow out any remaining fluid.
After that, I put in household oil. That does the trick every time & keeps it running smoothly for a long time.
The whole process takes 5 minutes.