The context of the joke is the rivalry between two straight-laced and erudite ranking police officers, Captain Holt and Deputy Chief Wuntch.

The Victor Emanuel joke follows up on a much longer exchange, which goes like follows:

"You're like the league of Nations in 1936, hoping the Abysinnian crisis will just resolve itself."

"That is the lesson you draw from the fall of Addis Ababa? Raymond, you sound so naive."

"And you sound just like Victor Emmanuel the Third

A bystander who does not understand the reference later on uses "Victor Emmanuel III" as a generic insult.

From this context it is clear that the joke is not some obscure kind of rhyming slang as suggested by another post, but instead refers to the second Italo-Ethiopian war.

In the nineteenth century, as various European powers divided up the continent of Africa among themselves ("The scramble for Africa") the recently united Kingdom of Italy tried to conquer the Ethiopia. In a unique turn of events, the Ethiopians defeated the Italians in the battle of Adwa and preserved their independence.

This thread with posts by u/khosikulu offers some more explanation of these events.

Losing to an African nation was seen as very humiliating in the racist and imperialist atmosphere of early 20th century Europe, so when Mussolini took control of Italy in the 20s, conquering Ethiopia became an important goal of the new regime. They build up their forces, found an excuse to attack, and invaded in 1936.

The Ethiopians gave it their best and scored some successes, but between the Italian army's more modern weaponry, airpower, and the use of poison gas, they lost.

During the conflict, the Ethiopian emperor Haile Selassie appealed to the League of Nations several times, including a very famous speech at the end of the conflict. The League applied sanctions to Italy, but these were ineffective and Ethiopia was occupied until World War 2 restarted the conflict and brought British aid to drive the Italians out.

This event and the failure to take action against the Japanese occupation of Manchuria have become the most iconic examples in popular perception of the failure of the League of Nations.

For much more detail on these events and the international reaction, read these posts by u/Colonel_Blimp

Now, to bring it back to the television show: The king of Italy at the time was Victor Emmanuel III. Upon the defeat of Ethiopia, he was proclaimed emperor of Ethiopia. Although not personally the chief architect of these events, he was seen as complicit in the fascist regime. For more information on Victor Emmanuel III himself and his role in Mussolini's takeover, see this post by u/Klesk_vs_Xaero

(Yes, they could just have said "You sound just like Mussolini," but that wouldn't have been obscure enough.)

As a side note, this joke is one of the things that made me fall in love with this show. It's funny even if you don't understand the background and just see these stiff-necked, hyper-formal, erudite weirdos have their very weird rivalry, but it's even funnier when you do understand the background. And then a minute later Holt realises that Wuntch's name rhymes with "Lunch" and is absolutely amazed by that.