The Edessan Guards aren't real. The canons of the Holy Sepulchre could refer to two separate things, neither of which are really anything like in the game.

I've never heard of "Edessan Guards" outside of the game. The County of Edessa was one of the crusader states, the first one to be founded, during the First Crusade in 1097. Some of the crusaders broke away from the main group and established a county around the Greek/Armenian town of Edessa in northern Mesopotamia. It was the furthest north and furthest east of the crusader states, and the biggest, with territory on both the east and west banks of the Euphrates River. The first count was Baldwin of Boulogne, the brother of Godfrey of Bouillon, the first ruler of Jerusalem further south. When Godfrey died in 1100, Baldwin became king Baldwin I of Jerusalem. Their cousin (well, some sort of relative), also named Baldwin, became count of Edessa and then also king of Jerusalem, and Baldwin II's cousin Joscelin succeeded him in Edessa, followed by Joscelin II. The Seljuks in Anatolia and Mesopotamia slowly chipped away at the county until the town itself was sacked in 1144, so it was also the first crusader state to be reconquered. Afterwards, the surviving crusader nobles of Edessa lived in the south in Jerusalem (including Joscelin II's son, who is usually known as Joscelin III, even though he never ruled in Edessa).

So although there were probably Edessan soldiers, and Greeks and Armenians came south to live and work in Jerusalem, including in the army, they were never known for being particularly elite soldiers. There was no "Edessan Guards" unit, and I'm not even sure what the game is referring to, if anything. I guess it just sounded cool?

The canons of the Holy Sepulchre could be two different things. When I first heard the term I thought it was hilarious because normally the "canons of the Holy Sepulchre" were simply the western European-style cathedral chapter that was established in the Church of the Holy Sepulchre in the early years of the Kingdom of Jerusalem. The Holy Sepulchre became the cathedral of the diocese of Jerusalem, governed by the Patriarch (basically just an archbishop with a fancier title because it was Jerusalem). As in Europe, the cathedral was given a "chapter", which means the priests and other church officials who worked there and administered the actual building as well as the diocese in general. They were also responsible for electing a new patriarch whenever one died/resigned. When Jerusalem was lost in 1187, the cathedral chapter moved to the new capital, in Acre, which caused lots of problems because Acre already had its own cathedral with its own chapter. The members of the chapter are known as canons, so that's what I was thinking of - a bunch of priest-administrators, now turned into a military unit in the game.

But what I imagine the game is actually referring to is the later Order of the Holy Sepulchre, which was founded in the 14th century, long after the crusaders had been expelled from Acre and everywhere else on the mainland. Latin Christians were still allowed to visit the Holy Sepulchre as pilgrims, and sometimes they liked to perform a knighting ceremony there, so a sort of informal military order was created. They weren't really allowed to exist as a formal military order in Jerusalem - the other military orders, especially the Knights Templar and the Knights Hospitaller, were kicked out with the rest of the crusaders in the 13th century. The Order of the Holy Sepulchre liked to pretend its roots went all the way back to the First Crusade and that it was an actual organized military order, and it was eventually officially recognized by the church, but it was really only founded in the 14th century and it never fought in battles.

So in short, there was no such thing as Edessan Guards, and the two things that could be called canons of the Holy Sepulchre were also not really military units.