So, elemental fury cannot be used on enchanted weapons. That being said, what happens if your other hand weapon is enchanted and other hand weapon is not? Does it affect according to right hand? (The dominant hand) Do both hands need to be non- enchanted?
Or does it just simply affect that (those) weapon(s) which are non - enchanted even if other was enchanted and the other wasn′t?

I′m asking this because I was thinking if it′s possible to use a non - enchanted dagger in left hand and enchanted axe in right hand and still use the Elemental fury shout to boost your attack speed?

Because I know that left hand weapon affects dual wield attack speed and right hand weapon determines the damage on dual wielding power attacks when both attack buttons pressed. That′s why I was wondering if I could use this kind of trick to increase the speed even more.

You can enchant one of the weapons and still use the shout. I just don't remember witch one you enchant you'll just have to test it or someone else, I'm sure will post it.

off hand not enchanted = u can use elemental fury
or so I've heard

Sounds pretty sick. In a good way^^ Too bad I don′t have a dual wielding character with speed perks and the shout.
My guess would have been that right hand needed to be non - enchanted but I have to trust you guys No experience with that personally.

The elemental shout effects any weapons you have out that aren't enchanted. But when dual wielding, the weapon in your off (left) hand determines the speed of the dual wield attack and power attack.

So you can enchant your right handed weapon and leave the left handed weapon unenchanted (should be a dagger for maximum speed) and you will get very fast dual wield power attacks and dual attacks (both triggers used at once).

This is the core of what I need to know Combined with the Shout, right?