Is there a grease plug or how to grease a gearbox of a 1990 Chevy Cavalier 5 spd

There is a grafite lubricant that is used on motorcycle cables which would be best but there is a little tool nedded to attach around the cable then add the graphit lubricant. Have you taken the cable off the neutral safety switch to verify that the cable is actually your problem? I have seen guys spray wd40 down the cable but thats up to you.

With the engine off , does the shifter move freely? If it's only hard to shift while running , maybe it has got the incorrect trans fluid/oil in it?

Try pumping the clutch pedal, about 10 times before shifting next time, to see if it helps. Hyd. clutch may give trouble after sitting over night. Then be ok while driving! Problem more pronounced when cold. (maybe) Like answer 2 suggest, try shifting with eng. off to see if it shifts ok. Then try it with eng. running. If it is different, poss. clutch or lube problem! I don't think it is a shift cable binding when cold.