I believe that the nature of deity is both unknown and unknowable (by humans).
As I understand it, "the nature of deity is unknown (and may or may not be knowable)" equals 'soft' or 'weak' agnosticism, and my position is 'hard' or 'strong' agnosticism. I was a soft agnostic up until relatively recently.
(Quick aside: that terminology bothers me because it's possible to be a strong weak agnostic -- i.e. you believe very strongly in the soft-agnostic position -- or a hard soft agnostic, or also a soft hard agnostic ("I'm pretty sure the nature of deity is unknowable as well as unknown"). Not sure what would be good alternative terms, though. Also, hard agnosticsim != militant atheism.)
I've been fairly sure for many years that the nature of deity is unknown, what with implausible theologies and the power of science, etc etc, blah blah woof woof -- this argument has been made, and people have responded to it, a million times.
There are two possible arguments, I think, for why we cannot know the nature of deity (as opposed to merely "we don't know it, but we might figure it out"). One is the "perverse liar god" argument, and it's sort of tongue-in-cheek. If there's an omnipotent deity, then it could make itself unknowable, never mind why it would want to. It could even put on an understandable mask while leaving its true nature hidden.
The other possible argument is "fundamental limits of human understanding". The human brain may be the most amazingly complex awesome thing in the universe, capable of conceiving arbitrarily complex and abstract ideas... but is it capable of understanding something omnipotent, omnipresent, omni-everything, possibly vaster than the universe? I highly doubt it, given how hard it is to truly grasp (say) the sheer size of a galaxy. (And I do mean truly grasp. Saying "oh, it's so many frillion light years across" does not count.) A galaxy has got to be a lot smaller than an omni-deity.
You'll note I said "fundamental limits of human understanding", not "fundamental limits of any understanding". I don't doubt that an omnipotent deity could understand itself perfectly well. It's perfectly possible that there are forms of understanding out there that are orders of magnitude more powerful than our piddling little thoughts, or maybe even have a completely different basis -- call them "super-understanding". But given that humans are limited to human understanding, can we understand super-understanding? I doubt it.
(For a very readable, math-flavored analogy to the topic of super-understanding, see Scott Aaronson's fabulous essay Who Can Name the Bigger Number?, which you should read anyway. He discusses Turing machines and Super-(Super-Super-...)Turing machines, among many other fascinating topics.)
And by the way, I have high standards for what I'm willing to call understanding deity. I'm not willing to settle for a grammatical string of English words, or a bunch of math, or whatever, that describes deity perfectly. I am perfectly capable of 'understanding' (sneer quotes!) a sentence like "God is a spirit, infinite, eternal and unchangeable, in His being, wisdom, power, holiness, justice, goodness, and truth", in that I know what all its words mean and I can parse the sentence, because that is perfectly fine English. But can I fully appreciate the impact of a spirit, infinite, eternal and unchangeable, in its being, wisdom, power, etc? Can my body generate a sufficiently large visceral/emotional reaction to the import of that idea, or will it run out of neurotransmitters first? Can my humble heart and mind contain the infinite? I think not.
Now, since I'm feeling a bit Hofstadterian, try this one on for size: "God is a spirit, infinite, eternal and unchangeable, in His being, wisdom, power, holiness, justice, goodness, truth, abstraction, recursion, subtlety, and inscrutability." Can this new, improved sentence give us a true, visceral understanding of an omni-deity? It's certainly an improvement.
(God-sentence is from Chapter 7 of Anne of Green Gables. I love that book.)