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 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.
