This is one of the more famous of the set of extraordinary words that were coined in America in the early years of the nineteenth century, along with such gems as absquatulate, hornswoggle and skedaddle.
As well as its literal meaning of a heavy or knock-down blow, sockdolager also came to mean something that was exceptional in any respect, especially, the OED says, a particularly large fish. James Fenimore Cooper wrote in 1838 in Home as Found: “There is but one ‘sogdollager’ in the universe, and that is in Lake Oswego”. A related sense given in Bartlett’s dictionary in 1848 was “a type of fish hook”
Lexicographers are reluctant to speculate about where it came from (as usual there’s little evidence), but we may hazard a guess that it’s a combination of sock, meaning to give somebody a blow, with doxology, the little hymn of praise sung towards the end of a church service. Researcher Barry Popik found this more detailed speculation in the issue of the Chicago Daily Tribune of 19 March 1893:
A writer in the March Atlantic gives this as the origin of the slang word “socdollager,” current some time ago. “Socdollager” was the uneducated man’s transposition of “doxologer,” which was the familiar New England rendering of “doxology.” This was the Puritan term for the verse ascription used at the conclusion of every hymn, like the “Gloria,” at the end of a chanted psalm. On doctrinal grounds it was proper for the whole congregation to join in the singing, so that it became a triumphant winding up of the whole act of worship. Thus is happened that “socdollager” became the term for anything which left nothing else to follow; a decisive, overwhelming finish, to which no reply was possible.
The particular claim to fame of sockdolager is that a close relative of it was supposedly almost the last word President Lincoln heard. In Tom Taylor’s play Our American Cousin, there occurs the line “Well, I guess I know enough to turn you inside out, you sockdologising old man-trap”, and as the audience laughed, John Wilkes Booth fired the fatal shot.