How can the logical impossibility of infinite self reference be reconciled in the case of God? This assumes that God conforms to the laws of logic as without doing so we can make absolutely no deductions about him, his existence, or any of his actions or attributes.

Within computer science, there is the notion of computability. This is the idea of whether it is possible to calculate something or not. It is provable that there exists a set of problems that cannot be computed. See the Halting Problem

If we take the attributes of the traditional Christian god, that he is all knowing, and all powerful, it appears this creates a logical contradiction. Here is an example:


Event A causes event B within the universe.
God decides that he does not want event B to occur so he stops event A from happening.
Event A no longer happened and therefore God would never intervene in the first place. Go to 1.


This is a very simplified example, and suffers from the problem that it is grounded in the concept of time, and this would imply God is able to circumvent this paradox because of the fact he is outside of time.

However effectively the same occurs with the halting problem, except time is not an issue. If God evaluates the universe (all of space and time) and comes to a decision, he takes action but some actions will depend on what he originally observed meaning it must be re-observed and re-evaluated. In this 'new round' of observation he is now evaluating himself and his previous actions. In some cases, this can lead to infinite self reference which is logically undecidable.

This seems to leave us with 3 options:


God is not all powerful. He could be very close, but with the diagonalisation proof I think we can show there are conceivably situations that would not work.
God is not all knowing. Again, he could be very close to all knowing, but can't logically be entirely all knowing.
God does not conform to the laws of logic.


I would be really interested to hear any thoughts you may have on different parts of this. If anyone here has studied the halting problem in more detail than I it would be interesting to see where it doesn't hold.

Edit: I feel I should make a small clarification about the logic assumption. If you actually know what logic is, and I don't mean "things feeling scientific" or something wishy washy like that, I mean the laws of logic, then I think you will realise that saying God does not conform to them effectively makes the concept of God pointless.  

I know Christians who agree and disagree with this, but it seems that the pattern is those who actually understand what logic is agree that God must conform to it.  

It is possible to say that God does not conform to logic, however if you believe this you must also accept that, from our point of view, we can then say nothing about his nature, his actions or his existence. 

I don't think this path of reasoning benefits anyone in any way.

Edit 2: Here is a short description of the halting problem. The analogy I am making is that God is essentially one of the 'oracles' referred to in the article, and after acting within the universe must re-evaluate the universe to see if more changes need to be made now that he can see the results of his actions, thus leading to self-reference.
Nothing to do with religion / God / whatever, but there seems to be a fundamental flaw in your argument here.


  
  Event A causes event B within the universe.
  God decides that he does not want event B to occur so he stops event A from happening.
  Event A no longer happened and therefore God would never intervene in the first place. Go to 1.
  


The third bullet does not follow unless you are thinking of God as Marty McFly hopping backwards and forwards.

If I have misinterpreted the logic in the question, please let me know. However, let's put this into more common terms, following your reasoning:


smoking (A) causes cancer (B) and costs money
I decide that I don't want to get cancer or waste money, so I stop this from happening to me by not smoking
I didn't smoke (!A) and I find I don't have cancer (!B) (based on a statistical average) and have spare change in my pocket, therefore my efforts were wasted and there was no need not to smoke


or:


leaving the hob gas on unlit (A) causes houses to explode (B)
I decide I don't want my house to explode, so I check the gas is off when I'm not using it
the gas wasn't on (!A), and my house didn't explode (!B), therefore my caution was unneeded and there was no need to turn off the gas


Even in Human logic, the third bullet is nonsense. It really isn't my intent to defend the religious view here, but this is not a sensible argument against God, and is trivially dismissed even when considering a person with natural knowledge. If we pre-suppose all-knowing, then that not includes possible consequence, but rather: absolute knowledge of consequence (and prior reasoning).

It seems that even in the knowledge that A (and B) hasn't (haven't) happened, having A continue to not happen (to avoid B) is still necessary.