I was planning on making a barbarian using a geared up immortal king set.
My two questions are...

How rare is this set?

Is it viable since it takes up all but the ring and amulet slots?

The + to damages, skills, and strength is just too good to ignore however.

Fairly rare, but not impossible - especially since lots of people are in Hell now. You should be able to find someone to set you up once you get big enough to wear it.

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People who live in cinder block houses can throw whatever they want.

And yes, it's extremely viable. Good dmg, good speed etc etc.
The helm and armor is the only pieces that can be a bit hard to find.