Mount&Blade/Khergits

The Khergits have strong cavalry as well as horse archers. Their biggest weakness is a lack of infantry.

Against infantry
Your favorite opponent. Khergits horsemen and lancers should make short work of most infantry. Just set them to charge and watch the fun. You might also consider joining them as well.

Against cavalry
Your cav. should charge if the enemy is lighter armoured, but against knights I'd not send in my tribesmen, maybe only lancers, horse archers and vet. horse archers, however should be able to unhorse the foe, or even better, unfoe the horse.

Against archers
Lead your army using the F2 (follow me) command on an angle to the archers. If terrain permits, try to put an hill between yourself and the archers. Just try not to start a battle going uphill. If you have a choice between leading the archers up a hill to save yourself some shafts and keeping them on level ground, give the hill a miss!

Against ranged horsemen
Only the veteran horse archer gets access to coursers, meaning that if the enemy force consists mostly of regular horse archers your best bet is to send in your fast lancers and yourself on a spirited courser. If however the force consists mainly of veteran horse archers, who also have coursers, your best bet would be to fight in a valley or at the edge of the map, since their ability to move away from your cavalry is their main advantage. The poor AI quite often gets its mounted units trapped against walls, making them that much easier to kill.