Predicament, dilemma, quandary, plight, scrape, fix, jam, pickle can all denote a situation from which one does or can extricate himself only with difficulty.
Predicament carries the implication that the situation constitutes a problem for those who are involved in it and may additionally imply lack of freedom to do what one wishes or finds essential for some reason, or it may imply deep perplexity as to ways out of the situation.
Dilemma applies to a situation which constitutes a predicament from which one can escape only by a choice of equally unpleasant or unsatisfactory alternatives.
Quandary differs from dilemma chiefly in its stress on puzzlement or perplexity; in fact, this implication is often so emphasized that the suggestion of a dilemma or an unavoidable choice between alternatives is lost or obscured.
The remaining words all definitely imply a difficulty, often a very disagreeable situation.
Plight suggests an unfortunate, trying, or unhappy situation.
Scrape applies to a specific difficulty in which one is involved through one’s own fault; often it suggests a being in disgrace or disfavor.
Fix and jam are somewhat casual terms that stress involvement and entanglement from which extrication is difficult.
Pickle applies to a particularly distressing or sorry plight.