Crush, quell, extinguish, suppress, quench, quash are comparable when they mean to bring to an end by destroying or defeating.
Crush in this sense retains from its basic meaning the implication of being destroyed or injured severely by pressure from without, but it differs in being more often applied to immaterial than to material things and in implying a force at work that makes for the destruction of effective opposition or operation especially by preventing resistance or by depriving of the freedom necessary for expansion or thriving.
Quell means to overwhelm completely and reduce wholly to submission, to inactivity, or to passivity; the term may be used in respect to people or animals or to (usually immaterial) things; thus, one may quell a riot or the rioters; quell a mutiny or the mutineers.
Extinguish (see also ABOLISH) implies an end as sudden or as complete as the blowing out of a candle or the putting out of a fire with water.
Suppress differs from crush especially in implying conscious action, in more strongly suggesting a power or force that openly quells or extinguishes, and in more often taking as its object a definite objective person or thing.
Quench, which is close to extinguish in its basic meaning, differs from it in extended use in stressing a satisfying, dampening, cooling, or decreasing (as of ardor) as the cause of extinction. Although it is used specifically of thirst, it is also frequently referred to emotions, sensations, and desires.
Quash basically implies a shaking or dashing that destroys; in the present sense (see also ANNUL) it implies a sudden and summary extinction.