You may have decided to support the claimant a bit early. There's really not much you can do when all you have are 90 units with 1 lord vs 600 and 9 lords unless your party's stats (like surgery/first aid) are super high already.

Here are some tips that may help you out:

1. A max army size of 90 means that you don't have enough Renown and Leadership. A good army size to have when declaring for a claimant is at minimum of 150. Next time you should try to boost your renown (by taking fewer units into battle against a higher number of enemies). Having a renown of 1500 to 2000 is probably a minimum before striking out on your own. Also, put more points into leadership/charisma.

2. Try to build up relationships with the lords of the faction your claimant is from (capturing and releasing them repeatedly will gain you relationships fairly quickly as well as improving your honor). If you do that, you can visit their lords while they are in their castles and persuade them to join your cause. This will increase your holdings and lords without having to fight them. Since you'll always be the marshall of your faction, you can then ask your lords to join you in battle.

3. Use only high tier units and play to their strengths. For the Nords, their best units is huscarls, but they aren't mounted so suffer when fighting in the open. Your best bet is to fight in moutnaineous terrain and tell all your units to hold out on top of a hill. This will drastically slow any mounted units heading at you, giving your huscarls plenty of time to throw their axes for tons of damage.

4. Try to wait until there's a war between Swadia and someone else, when their leaders are distracted, go in and take their territory. Also, wait until you see Swadia conquer a city, this is the best time to go and take that city from them as it won't be heavily defended.

5. There are also some really cheap tricks you can do to take a castle without any losses, but that requires you to get some rhodok sharpshooters first. Just tell them to use their melee weapons and defend at the start of a castle battle. They'll be nearly invincible when hiding behind their board shields. Then wait until the enemy runs out of missiles, then tell them to open fire. After your guys run out of missiles, retreat, and repeat.

From the Mount and Blade wikia:

Leader skill

Like a party skill, a leader skill grants an ability to a party. However, only the party-leader's level in the skill is used.

I can confirm this, as several of my party members have 2+ points in Prisoner Management, while I only have 2 points in it myself. I can still only hold 10 prisoners.

If you're wanting your other heroes to be more beneficial to your overall party, you'd be best giving them party skills instead. If you want them to be of more use on their own (as a vassal for your kingdom), give them Leader skills, as they will then be the leaders of their own armies.