The criminal trial of Trump associate Roger Stone is to begin Tuesday in Washington, one of the last loose ends stemming from special counsel Robert Mueller’s investigation into Russian interference in the 2016 election.

Among the characters expected in featured roles: a defendant so renowned for his attention to sartorial detail that he stars in a video, “Roger Stone Explains How to Dress for Court”; a judge who despaired in pretrial hearings of what she called “middle school” antics; prosecutors who want to show the jury...