The History of the Six Knightly Orders of Calradia
For this logical explaination of how the knightly orders work, and how they were formed, we have to assume a few things about Calradia that were true in medieval Europe:
1. That Calradia has at least one monotheistic religion, (i.e. like Christianity, Judaism, and Islam, they all believe in the one god theory.) and that the "great prophet" of said religion did his important religious events in a place outside Calradia, and there are "sacred" places that followers of this religion go to visit, on pilgrimages.
2. That the old Calradian Empire, was basically the Roman Empire, and as such, had soldiers organized into legions.


The Great Legions of the Calradian Empire:
The fall of the Calradian Empire was a slow and drawn out one. It did not all disappear at once, it just slowly ceased to matter. We all know the Calradian Empire had a strong military force, composed of many legions of men. Certain legions became distinguished, and instead of being ordered numerically, were given unique names, Hence the six great legions of the Calradian Empire were:
The Lion Legion
The Bear Legion
The Raven Legion
The Leopard Legion
The Wolf Legion
The Eagle Legion

The Calradian Empire did not fall because it was beaten by a greater military power, it fell because of economic and political instability, while still trying to maintain it's great armies. So it eventually came to a point, where the only thing keeping the Calradian Empire alive were it's six great legions, but the legions themselves were falling into disuse, and they weren't being well maintained anymore.
Slowly each head commander of the legions broke off ties with the nearly gone Empire, converted themselves to a rising trend in military formations, a heavy cavalry focused army. Seeking employment and a sense of purpose, they offered to the Calradian religious order to act as safeguards for the long, harrowing and treacherous journey that it's followers take to visit the holy land.

Through a series of clever ideas about how to protect and transfer the value of the pilgrims wealth, they instituted a system of banking. This allowed them to fund their armies, and set up hospitals and other amenities that made the path to the holy land a much safer journey. The Legions (as they were still called) grew into quite powerful entities, bordering on the level of being equivalent to a full-fledged kingdom's power. This caused the ire of the other kingdom's of Calradia, who sought to eliminate the potential threat these legions could pose to their rightful claim of the throne of all of Calradia.

During this time period, the code of chivalry was invented, and instituted for much of the heavy cavalry soldiers of Calradia. Since the legions were so focused on a heavy cavalry doctrine, they too adopted the code of chivalry and reformed them selves into knightly orders, becoming:
The Order of the Lion
The Order of the Bear
The Order of the Raven
The Order of the Leopard
The Order of the Wolf
The Order of the Eagle

For a long period of time the kingdoms of Calradia worked to dismantle the six knightly orders, and after much work and subterfuge, they succeed, only a few months before you (the player) arrived in Calradia. Shortly after your meeting with the town merchant you hear the news that the six knightly orders have been "eliminated," and that they are no longer significant powers in Calradia.

Momentarily defeated, the two highest ranking officers of each order set out on a quest to find anyone, who could help them restore their orders to their former glory.



How the Knightly Orders of Calradia Work

The orders themselves are not slaves nor servants to the kingdoms of Calradia, so you can not actively order them around and make them your army as you please. When recruiting one of the head knights of the order and granting them a fief, you allow them to open a chapter house there, and thus form an army of the knightly orders troops. The knights don't directly serve you, but as you are their benefactor, they seek the same end goals you do, i.e. your kingdom becoming ruler of all Calradia, and they will help you in this pursuit as long as you respect their independence.

So while you can not actively recruit and raise the orders as armies of your own, you can have a few of their men join you by rescuing them from prisons and bandits.

The orders still have a small presence of military power in Calradia and still try to pursue their task of escorting pilgrims safely to the holy land, so you can encounter them in field, protecting their pilgrims from bandits. (Essentially they are manhunters, they fight bandits, but they arent too numerous, so they shouldnt provide to much competition for you, just help hold back the bandit horde.)
Each order operates primarily in a only one kingdom per order, so you are most likely to encounter the orders in the following kingdoms:
The Order of the Lion: in the Kingdom of Swadia, fighting forest bandits.
The Order of the Bear: in the Kingdom of Rhodoks, fighting mountain bandits.
The Order of the Raven: in the Kingdom of Nords, fighting sea raiders.
The Order of the Leopard: in the Kingdom of Vaegirs, fighting tundra bandits.
The Order of the Wolf: in the Khergit Khanate, fighting steppe bandits.
The Order of the Eagle: in the Saranid Sultanate, fighting dessert bandits.

The orders are all roughly the same military wise, they all have powerful heavy cavalry, strong infantry, and well trained crossbowmen.
The orders primary task is to escort pilgrims, so you will always encounter pilgrims as fairly large parts of their "forces." Pilgrims wear pilgrim attire, and carry some peasant tools that can be used as weapons, like pitchforks, knives, and hunting types of bows and crossbows. Some may be lucky enough to have picked up a shield along the way.
Each order has either adopted some of their home kingdom's tactics, or other unique units, each order has a unique tier 2 unit, that differ entirely between orders.
The Order of the Lion: Balanced effective tier 2 militia units, tier 3 footmen who use prefer maces and tier 4 heavy infantry who employ powerful two handed swords.
The Order of the Bear: Tier 2 Merchant Cavalry Militia who are well equipped but poorly trained for cavalry, tier 4 sword and shield heavy infantry.
The Order of the Raven: Tier 2 Widows of many a Nordic warrior who carry some of their fallen husbands equipment into battle, tier 3 footmen who prefer axes and tier 4 heavy infantry who specialize in throwing axes.
The Order of the Leopard: Tier 2 Clergymen who provide religious services to the order's troops in the field and during battle, tier 4 pikemen, tier 5 dismounted knights who prefer to use poleaxes on foot, tier 6 knights who have the heaviest armor of all the knightly orders.
The Order of the Wolf: Tier 2 pike men, tier 4 heavy sword & shield & bow & arrow infantry/archers, tier 6 knights who forgo shields in favor of being able to use bow & arrows on horse back.
The Order of the Eagle: Tier 3 footmen who prefer spears, tier 4 heavy javelineers who act as first strike infantry. Technically the Order of the Eagle doesn't have a tier 2 unit, but rumor has it that an order of assassins have blended in with the pilgrims and the order overlooks them as long they don't cause trouble and fight against any who try to waylay the pilgrimage.

"Technically" tier 1 and tier 2 units arent all "actually" members of the order for roleplay purposes (except lion militia, wolf pikemen) and the orders troops really start at the footmen and crossbowmen, but its easier to have a balanced upgrade tree with very weak starting units that get better over time, as opposed to starting at mid grade power units. so the individual "pilgrims" dont become merchant cavalry, and then footmen, just that persons spot in the army is "replaced" by someone else.