Its been a while, so trying to remember exactly what I did, but I had same problem.
Took the cable out, wiped it down good to get all the old grease out/off. Kenny at Emerald Coast let me borrom a "reaming tool" I think it was called. Greased it up with aqualube, put it back in. Worked a lot better. Unfortunately mine was all galled up and I ended up replacing it anyway.
Not if you consider the cost of the cables failing at THE worst time! Ive lubed,beat, and heated my cables to prolong life but have always replaced them in the end. Cost depends on what type you have. Worm style drive is very inexpensive under about 18 ft. I would replace them as they are easy to do and find. J
If you pull the cable out of the motor and it is easy to turn, the cable should be fine. If the engine is tough, then the steering tube on the engine is full of gummed up old grease. If the cable is only stuck in the tilt tube, then you may get away with reaming/cleaning it if you do not damage the cable removing it. It is not hard to replace a cable, but sometimes you have to remove the engine to change it to give you enough clearance to get the cable in and out. If the cable is old, I would think about changing it. If I know what cable you need, I'll see what I can get one for.