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Next time, don't check a dictionary or thesaurus, look up the etymology."Plight" means that someone is in a desperate situation, and may suffer loss, come to harm, or even die if they do not get help. The original meaning of "plight" was to be in danger.
"He was reduced to begging on the streets, looking for scraps of food, and there was no one to help him in his plight."
"The tigers in this region are nearly extinct, but man continues to ignore their plight."
"Predicament" is a situation that is not necessarily threatening, just hard to deal with, or hard to decide on. For example, you might be accepted to a really good college after promising your father or mother you would go to another, this is certainly a predicament, but definitely not "plight". A predicament usually does not carry with it a sense of danger, just the need to make a difficult decision or choice.
"Quandary" originally means "perplexed", as in confused, or unable to find an answer. From a literal question, this has been extended to the "question" of what to do in a situation.
Any situation that is sufficiently complex or confusing can leave you in a quandary.
An ordeal is not really related to these other words. An ordeal is a very difficult, trying experience, especially one that is physically or emotionally traumatic.
You should note that ordeal originally meant punishment that was handed out to someone, then it seems to have taken on elements of a "test of character" and finally the modern meaning of just a really difficult, trying experience.
參考: I tutor English.
I use etymonline.com to look up etymologies.