The word ‘sockdolager’ appears neither in Benson, nor in Wells, nor in Vikivortaro, nor in Vikipedio, nor in ReVo, nor in Sonja. So, how should it be rendered in Esperanto?

It's a peculiar localism which means the same as other extant words, I see no pressing need to render it into Esperanto.

What about, say, 'skrike'? That's a word from the area where I'm from and it means cry. Tell me why it would need a special translation above 'plori'?

Because some Christian worship services include a doxology, and these hymns therefore were familiar and well-practiced among church choirs, the English word sockdolager arose, a deformation of doxology, which came to mean a "show-stopper", a production number.[citation needed] The Oxford English Dictionary considers it a "fanciful" coinage, but an 1893 speculation reported in the Chicago Tribune as to the origin of the word as one of its early attestations

https://en.wikipedia.org/wiki/Doxology

https://eo.wikipedia.org/wiki/Doksologio

Roch:

Because some Christian worship services include a doxology, and these hymns therefore were familiar and well-practiced among church choirs, the English word sockdolager arose, a deformation of doxology, which came to mean a "show-stopper", a production number.[citation needed] The Oxford English Dictionary considers it a "fanciful" coinage, but an 1893 speculation reported in the Chicago Tribune as to the origin of the word as one of its early attestations

https://en.wikipedia.org/wiki/Doxology

https://eo.wikipedia.org/wiki/Doksologio

The verb sock ("to punch") and the noun doxology ("a hymn of praise to God") may seem like an odd pairing, but it is a match that has been promoted by a few word mavens when discussing the origins of the Americanism sockdolager. Don't be too quick to believe the hype, however. When a word's origin is simply unknown, as is the case with sockdolager, there's a tendency for folks to fill in the gap with an interesting story, whether or not it can be verified. In the case of sockdolager, the "sock" part is plausible but unproven, and the "doxology" to dolager suggestion is highly questionable. The theory continues to have many fans, but it can't deliver the knockout punch.

https://www.merriam-webster.com/dictionary/sockdol...

\säk-ˈdä-li-jər\

Might "dislodge" could have something to do with it...