Leo Tolstoy's novel "Anna Karenina" famously starts "All happy families are alike." But what readers may want to know is how alike are different translations of such foreign classics?

There are half-a-dozen English-language translations of the 1878 Russian novel available for sale online, including the 2001 version produced by celebrated translators Richard Pevear and Larissa Volokhonsky. An endorsement by Oprah Winfrey turned that edition into a best-seller, with more than 1.3 million copies in print to...