I agree that this is very difficult. One way I've found that usually works is to use context to determine the correct reading. Often one of the readings will have specific nuances that the others don't, so the context of the sentence can help you out.
One example that I personally encounter all the time is
汚れる. It can be read as both
けがれる. They both mean "become/get dirty". However, the latter carries the additional nuance of a moral/ethical "dirtiness"/impurity/uncleanliness/corruption/defiling. So in my Christian Bible, in places where it speaks of spiritual uncleanliness or impurity, it is almost always read as
- 汚【けが】れた霊 → Impure/unclean/"evil" spirit
- どのような人の死体であれ、それに触れた者は七日の間汚【けが】れる。民数記19章11節 → Anyone who touches any type of dead body will be unclean for 7 days.
- 女性を汚【けが】す → Rape/Defile a woman
Doing a really quick research of
こたえる seem to mean the same, but the latter appears to be somewhat antiquated/literary. While
こらえる carries the additional meaning of "supress/hold back", usually associated with some kind of emotion (
あくびをこらえる → supress a yawn;
涙をこらえる → Hold back tears).