This wording was in the glossary of the 2010 Rulebook, but I didn't notice it until just now when I saw it in the new player's guide.
Since critical hits modify damage dealt, does this mean that damage dealt to Justice League #46 Superman by his special power would not be affected by critical hits?
And would the same apply to WoS #31 Daken when he rolls a 6 for his Muramasma Decapitation special power?
In both cases, it seems to be a timing issue. Does the modification from a critical hit occur before or after the damage becomes unavoidable?

I don't think that it would ignore critical hits. The only reason I say this is because critical hits ignore the rule of three so the damage would have to be added after the attack is over. I Will say that Im not too sure about this answer.

Yes, but that's not really the question. The reason that the rule of three doesn't apply to critical hits is that the rule of three only applies to damage values, and critical hits modify damage dealt. That's a completely different situation.
Unavoidable damage is "damage dealt that can't be evaded, reduced, modified, ignored, or transferred." Critical hits modify damage dealt.

i think this falls under the thing they were discussing with the timing issue of Crit Hits, they are saying there is 2 different "Damage Dealt" and that this one would be the final one, so the first one can be modified.

I don't remember a ruling that there were two different stages of "damage dealt" but I think I only read about half of the critical hit thread that I believe you're referring to. I know that how it ended up being resolved was this line in the new player's guide:
I'll go check out that other thread, though.

As you noted, unavoidable damage can't be modified.

Normally, that would mean "modified negatively" by damage reducers (Toughness will not get you out of taking Mystics damage), but for those rare cases where there would be a positive modifier... well, that's still a modifier and unavoidable damage doesn't care one whit about those modifiers.

Just wanted to make sure it worked how I thought it did. In the Superman case at least, I could have seen a possibility that the entire damage dealt, including modifiers, would be transferred to Superman, and then become unavoidable.

I would have rule it that way too. I agree entirely that a natural roll of 6 on Daken's Murasama Decapition will prevent the (now unavoidable) damage dealt to be modified by a critical hit, but Superman's case is different in a very important way.
In short, the power doesn't turn the damage into unavoidable until they are transfered, and the modifier is applied before that because the power specifically says that it transfer "all damage dealt". So IMO, Superman would take the full wrath of a crit hit, because the mod to damage dealt would be applied first.
Do you really disagree with that, normalview ? If so, may I ask where I get this wrong ?

In the case of Daken, I think I agree that the d6 roll becomes unavoidable before the damage is dealt, and therefore, would not increase from the critical hit (as it cannot be modified).

With Superman, I think it's a different story. In that case I roll to attack Batman. I critically hit. My damage value is 2 so the critical hit means I deal 3 damage. The damage dealt is not unavoidable as of yet. It's only when Superman activates his power - which is only after you know the dealt damage amount - that it shifts to him (and it all shifts to him, as stipulated by the special power) and becomes unavoidable.

That's fine. The damage dealt in that case doesn't become unavoidable until after it is transferred to Superman... so up until that point, when it is still just plain ol' damage dealt, it can be modified.

But after it is transferred to Superman, if another modifier were to come along at that point, no more modification.