Typically when this happens to me, I just accept my crew will nearly get wiped out. I would stand and fight for I think you have a chance of winning. First off, get you people to bunch up. Use the stand closer command 4 or so times right off the bat. Do not let you folks charge.
Secondly, what behind your folks. If the terrain is favorable, try to move onto a hill so they can't charge up it. Note that time will be a factor of course so you best bet may be to stand firm. Also, I hope you have a polearm with you. It's good to smack a horse in the head and stop it so you people can take it down, if not you. I've had to use my great lances this way when I"ve had my horse shot out from under my by the Khergits. Also, try to to keep your back to your guys and watch your six. The little devils love to come up behind you with a lance.
The good thing is, your skirmishers and militia pack crossbows some you'll have some exchange when they try to arrow you. Lancers do like lances though, watch for ;em. Just remember, keep it tight. Do not wonder from your people and stick with them. Also make sure they don't wander off. More than likely, if you keep a good formation, the initial charge will get stuck in and you can take down a few then.
If you don't pack a crossbow, wait for one of your people to die and pick their up and bolts, provided they are there, if you're not pulling pike duty. I'd also try to fight with your infantryman. He maybe the key. Keep him alive. Personally, I think you can get away with it with about 70 percent casualties. If you have a horse, you can also try to play, "I'm the target."
What I will do it try to pull them off, get them to chase me. Then I maneuver around my group so they can use enfilade fire or flank strikes. I hope you also have a shield.
One other good place to hole up is a group of trees. Trees are you friends! Khergits, well any horseman, has a hard time manuever around them. They will often hit them and stop at which point you may be able to take them out. As a matter of fact, I've use this tactic when fighting steppe bandits by myself. I find a clump of trees and start doing figure eights in them. Really messes with the AI. This and boulders.
So, depending on your battlefield, you need:
1. Formation
2. Terrain
3. Stay together. They're not players so they're not to particularly bright.
4. Unhorse them. They lose all their advantages.
Also, hit them in the head if you can. Khergits don't like helmet hair. One other thing you can do if you're mounted and the Khergits are close to your group. I call it maneuver 27 B. If they don't have a lance <-- important note - it really hurts otherwise, just pull out in front of them. Let them T-bone your horse. They stop, rear, and your guys swarm them. Works great with cavalry. I do it all the time with my knights. They have a hard time catching them so, I just find a group, run interception, and stop in front of the Khergits and watch them get lanced from behind.
