I take it that you think it couldn't. Which makes it not quite so omni, I guess.
Another way to try understanding the word omni is to conceive of possessing unlimited intelligence, strength, wealth, beauty ..... whatever we deem valuable and desirable.
So in regards to square circles and such, it boils down to whether one regards the absence of square circles arising from our current shortage of strength, wealth, intelligence etc, or does the problem lie on the fundamental principle of relationship between "things and values"? So the reason you can't have square circles is because such a thing, if it would exist, would destroy the values by which we identify it in the first place (thus square circles illustrate the limitations of meaning, and not power, omni or otherwise).
On the topic of suffering, though, are you saying that ending human suffering would be a logical contradiction analogous to creating a square circle? If so, you probably need to unpack the contradiction for us.
Its quite a big topic to unpack, because there is an inextricable link between knowledge and action (or desire). The short version is that to have free will means that we must always follow our sense of benefit (desire), thus, being robbed of the possibility to pursue benefit (regardless whether that benefit is rightly or wrongly anticipated), or even robbing one of the consequences of benefit, effectively robs one of free will.
The longer version:
If you remove a fish from water, there is no means to relieve its suffering on account of it being outside it's natural position. If a fish, by its free will, flops out of the water on the river bank, it is the one engineering its own suffering. If our free will is inextricably connected to our sense of benefit (for better or worse), we require the equivalent of river banks or sea shores to flop about pitifully on (since sailing around in water in pursuit of a river bank would just be another type of suffering). IOW to have free will aligned to God requires the existence of an environment to manifest the opposite tendency. Technically that is impossible (where could one go to pursue the desire to be independent or outside of God?), so an element of (divine) ignorance is required to facillitate the desire of the living entity. So rather than
real river banks, the (fish like) living entity experiences virtual ones (ie, the suffering is experienced through an illusory sense of self in a specially designed world). Of course its not all 100% grief (since that would be just as equally useless as trying to bring free will to its proper application as desperately swimming around in a shoreless ocean). But, whatever happiness this existence affords, it is always beseiged by a sort of suffering, since, at its core, this existence is built on the premise of being separate from God.