In the OED, the first definition of raree-show is straightforward, dating from the seventeenth century: “a set of pictures or a puppet show exhibited in a portable box for public entertainment; a peep show.” That latter phrase has salacious modern connotations that Sterne may have been toying with. The dictionary gives nine citations between 1677 and 2003, including quotes from Tom Jones (1749) and Walter Scott’s Peveril of the Peak (1823).
The second definition is even closer to Sterne’s sense: “an exhibition, show, or spectacle of any kind, esp. one regarded as lurid, vulgar, or populist.” We get this usage in a letter of Edward Fitzgerald’s published in 1889: “Do you see Dickens’ David Copperfield? Carlyle says he is a showman whom one gives a shilling to once a month to see his raree-show.” Unexpectedly, the word shows up in William Gaddis’ The Recognitions (1955): “He’ll show you... He'll put up a real maudlin raree-show for you.”
In the third sense, raree-show is1681—2003 “a mass noun: spectacular or lurid display,” as in an 1809 letter by Scott: “Those immense London Stages fit only for pantomime and raree show.” Among the compounds are “raree-show box” and “raree-show performance.” Here, the dictionary cites Sterne’s usage. Now the reader can understand the word’s contemporary relevance and usefulness. Among our counterparts to the raree-show, to entertainments that are “lurid, vulgar, or populist,” are video games, Star Wars and the Harry Potter phenomenon, tacky children's concoctions consumed by adults.