Consider a barbarian wielding two axes. When he uses the Hammer of the Ancients skill, how is the damage calculated?
According to the Blizzard answer in this forum post
The damage of a skill modified by weapon damage is based on whatever weapon you happen to be swinging with when using the skill.
So basically it alternates between weapons in the same way as if you were using your normal attack.
The answer is that it depends on the skill.
For some skills, activating the skill is just like attacking - it alternates between the two weapons. So, for example, If your Demon Hunter dual-wields hand crossbows and then launches 4 Chakrams, 2 of those will use your primary weapon's modifiers (damage, attack speed, on-hit effects) and 2 will use your secondary weapon's modifiers.
Some skills, however, only use your primary weapon. These include, for example, the Monk's Cyclone Strike and Wave of Light. In general, skills that have a very heavy resource cost and/or a cooldown will behave that way. See this related question for the list of skills that behave this way.
Specifically regarding Hammer of the Ancients, I believe it belongs to the first category, and it alternates between the two weapons.
Hammer of the Ancients alternates between the two equipped weapons - I tested the weapon swing damage, I have different speeds on mine, opened the details tab and saw the 2 speeds changing with each swing.
If you are Dual wielding and you have 2 weapons equipped with the same DPS, but with different AS (Hammer + Dagger)
Hammer = 300-900 dmg AS = 1.0 => 600 DPS
Dagger = 200-600 dmg AS = 1.5 => 600 DPS
Using a skill like Frenzy (110% dmg )
You will first hit with your hammer (330-990) * 1 + (strength/100)
and second with your dagger (220-660) * 1 + (strength/100)
However if you use something with a cool-down like Furious Charge (195%) (10 sec cd)
you will hit only with your primary weapon
if it's a hammer 600 - 1800 * 1 + (strength/100)
if it's a dagger 400 - 1200 * 1 + (strength/100)
So the charge will do more damage if you have the hammer in your right hand.
Now scale it to earthquake (2000%) ==>
Hammer = 6000-18000 * 1 + (strength/100)
Dagger = 4000-12000 * 1 + (strength/100)
Considering that with the rune, Merciless Assault, if you charge 5 enemies = 0sec cd You can now spam a 600 - 1800 * 1 + (strength/100) AOE Attack that generate Fury :-D
Personally I use the same build as this guy So fun to play
And the tornados (sprint + Run like the wind) are taking my right hand damage.
What's cool about the dual wielding and this build is that you can have 2 weapons each with 500 life steal per hit and + 100% critical damage and this bonus applies to all the damage you do.