There are better resources than this forum to answer your question, google the mount and blade wiki or the taleworlds forums and you'll find a wealth of information.
For a few cents, instead, here is what you're in for:
Rhodoks: Cavalry-less. Strong and steady crossbowmen who aren't half-bad in melee, very sturdy spearmen infantry. Excellent against cavalry in the field, and at sieges due to their excellent crossbowmen. Poor against strong infantry, patricularly Nords.
Nords: Cavalry-less. Very strong melee, and infantry generally have a few throwing weapons. Their longbowmen are decent (3rd best after Rhodok and Vaegir), but can defend themselves in melee best of any, I think. I find them quite weak in sieges, attacking or defending, because of a general high-damage low-armour setup.
Vaegir: These are supposedly the best archers, though that is argued (bows run out of ammo a lot sooner than crossbows, for one factor). They have quite weak armour overall. Their infantry and horses are all quite weak in comparison to other factions, but some people like them for their versatility. Definitely best to use archer-heavy armies with these guys, and use the horses and infantry only to support them.
Swadians: Their foot troops are a lot like the Rhodoks, just a bit crappier in skill and equipment. They have incredible melee cavalry, however. A bit weak during sieges, but not as bad as the other horse-heavy faction, the Khergits.
Khergits: All-horse, except their recruit troop. They're a lot of fun, and can be the strongest in the field as long as the field isn't too obstacle-strewn. Only the Swadians freak me out when I player Khergits. They are very unwieldy to control, however, due to having only 'Cavalry' types. If you play 'em, make sure your Khergit Veteran Horse Archers can be switched to Archers, so you can direct them separate from your Lancers.
Sarranids: These guys have so-so infantry and bowmen, and strong cavalry. I would say that their cavalry are about equal to the Swadians' cavalry one-to-one, but they use swords instead of lances and thus have a bit of a weaker charge en masse. One major complaint about their bowmen is that they at certain levels can possibly spawn with javelins as a ranged weapon, making your Archers line a bit weaker (generally you'd want javelins in your infantry)
Did I miss one?