I was wondering how I could make a particle or material that looks like an air blast similar to the ones seen in Avatar, for example here Tenzin, Bumi and Kya vs The Red Lotus - YouTube and here.
If that’s impossible, then how might I go about replicating the shouts done in Skyrim?
Even though your questions is rather short, the answer could become a book on its own.
Besides proper meshes with proper materials moving in proper ways, you might end up using all kinds of splines in 3dsmax/maya/houdini, bake the animations into the vertices, set up complex shaders, and maybe it will look right.
I have been doing particle/effects for a while now, and personally find wind the most daunting thing to create.
Here are some links, one of em actually being my progress with wind… but so far… im still not satisfied.
As you can see, wind is like that golden egg, not many get it right 
Best effect might actually be from Epic’s fortnite and that was done with agnostic vertex counted animation. (basically baking the animations into vertices)
But that would mean you’d need to learn how to properly animate wind in a 3d tool first.
Thanks for the thorough explanation! I guess my best bet is to start looking for a real artist haha. I don’t suppose you’d know a cheap and dirty way of doing it would you? It’s not like the player would be staring at the effect I just need something more than a giant white sphere 