Offhand Weapon skill
Offhand Weapon skill is not much more of a weapon skill than Parry or Brawling, in that it doesn't require a specific weapon to learn just that you perform the action needed to learn it.
Offhand is often referred to as 'Dual Wielding' since one is capable of wielding a weapon in both hands and attacking with either one at any point in battle. The weapon wielded as Offhand can be anything from a sword to a throwing dagger (yes, you can throw with your off hand while still holding your main weapon in your right).
The main use of this system is training your secondary and tertiary weapons. While using a weapon offhand gives you an automatic 30% deduction in your ability with it, as you train your offhand skill you will notice this penalty less and less. The fact that using a weapon offhand lets you train not only the offhand skill but the weapon skill for the class of weapon you are wielding offhand makes it highly effective for training secondary and tertiary skills.
Since brawling skills can be learned while wielding a weapon in your right hand, there is no need to learn brawling in this fashion.
Dual weilding allows a fighter to hold a lower-skilled weapon in their left hand and a higher-skilled weapon in their right, parry is still counted against your right hand weapon so you count no penalty for training the lower-skilled weapon in your left hand.
To use the offhand skill, you must indicate that you wish to attack with your left hand. To do this, simply enter 'attack left' where you would typically enter 'attack'.
A good strategy for Dual weilding is to carry a heavier weapon in your right hand and a lighter one in your left. This allows you to change off, if you find your attacks are taking too long to execute, you can use the lighter weapon to attack faster. If you find your attacks arn't hitting hard enough, you can use the heavier weapon to cause more damage.
Combos in Dual wielding are simply maneuvered, as well. If both weapons are edged of the same size and type, slashing or thrusting, you simply follow your combo in a line no matter which hand you attack with. In the case of both weapons being edged, one being medium and one being light, you simply move to the next attack in the sequence for the weapon you are switching to. For example, if your right hand is Medium Edged/slicing and your left hand is Light edged/thrusting, and your last attack was a sweep (right), your next attack would be: thrust left. This will maintain your balance and make sure you're still in good position.
Other combinations of weapons are effective as well, it is fully possible to wield a longsword in one hand and a hammer in the other, provided neither is a two handed weapon. Thrown weapons are highly effective from offhand since you need not lose your parry weapon when you throw them nor do you need to wield a new weapon into an empty right hand.