1830, "a decisive blow" (also, figuratively "a conclusive argument"), fanciful formation from sock (v.1) "hit hard," perhaps via a comical mangling of doxology, on a notion of "finality." The meaning "something exceptional" is attested from 1838.

Sockdologising likely was nearly the last word President Abraham Lincoln heard. During the performance of Tom Taylor's "Our American Cousin," assassin John Wilkes Booth (who knew the play well) waited for the laugh-line "Well, I guess I know enough to turn you inside out, you sockdologising old man-trap." Amid the noise as the audience responded, Booth fired the fatal shot.