Is the height of races (men, elves, orcs, goblins, etc) ever mentioned by Tolkien? If not, did the movies just make up the certain heights?
Yes, he has, but as far as I remember, not for all the races.
Hobbits were 3 to 4 feet tall -- average 3 feet, 6 inches ( Letter #27)
Actual size – only important if other objects are in picture – say about three feet or three feet six inches.
Orcs were 3 & 1/2 to 4 feet tall ( The Fellowship of the Ring)
The size of the Elves and the men was similar. There was a mention I think that the dwarves had similar height to the Hobbits, if not slightly taller.