Operation Mincemeat: During World War II, British Intelligence Officers dressed up a corpse as a Royal Naval Attache handcuffed to a briefcase which contained a letter concerning the invasion of Greece and Sardinia from North Africa by way of the Mediterranean Sea. The body was dropped off the coast of Southern Spain in order to be retrieved by local authorities. After the British feign attempts to recover the body, a faction of Spanish Authorities sympathetic to the Axis cause, allowed the Nazis to examine the Naval Attache's personal effects. As a result, the Nazi High Command shifted military personnel from France to Southern Europe. The only problem was, the letter was a hoax, it was part of a disinformation campaign, to reduce the Axis military presence on French shores in order to pave the way for the Allied-led Invasion of Normandy.
The Irgun was a Zionist, or a pro-Jewish, guerrilla group that operated during the period before the formation of the Jewish State in 1948.
In the early years of the twentieth century, the Jewish community in Palestine, which would eventually become Israel, founded an organization called the Haganah (Hebrew for Defense), for the purposes of self-defense. In 1931, a group called the Irgun split from the Haganah to take a more militant stance against those who would persecute the Jewish people. The Lehi split from the Irgun for ideological reasons, they wanted to ally themselves with the Nazi Germany and Fascist Italy in order to drive the British out of Palestine, as well laying the groundwork for repatriating Jewish citizens.
Poxy is a UK slang term which refers to something unpleasant.
In this installment, it is revealed that a "Little Drummer Boy" is someone who bangs the drum to rally the troops in a call for action. In this case it is meant figuratively rather than literally. Moreover, "Little Drummer Girl" is a slight variation of a theme where Charlie's actions would inspire others to take up arms.