I have checked the dictionaries but these words still sound similar to me. Do you have any suggestion to help differentiate their meanings?
To me, plight and predicament are similar in many cases, except that sometimes I hear predicament in cases where the problem is more focused in the moment, whereas I often hear plight for something that is ongoing over the long term. Please note that that is just my initial thought, not a definitive explanation. Others might have a different take on it.
The slight difference that I see with woe is that it has an added connotation of grief.