Does the soak from Armor and Shielding Winds of Aqshy stack?

Yes.

I can't see any rule that forbids it. A wizard wearing armour is at a modest spellcasting and channeling penalty of course.

P.S. I would think that Shielding Winds of Aqshy cannot be bypassed by 'Ignore Armour' card results? I am right?

Fresnel said:

Depends on the wording of the card: some ignore only soak from armour, some ignore all soak.

Shielding Winds of Aqshy aren't armour, so they cannot be ignored by those cards, that ignore armour's soak.

D.