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.
- For Teachers