What major views are there on the question of whether God shares moral responsibility for our deeds, good and bad? I am looking for an overview of the major historical approaches to the following question/group of questions:

Since God has given us this body to do good or bad, then does he share at all in the praise or blame we incur for particular acts? And if he does, why is it that we are judged to heaven or hell based on those acts?

I realize the general philosophical nature of this question, but I assume that there will be a relatively small number of historically well-represented or well-supported approaches to the question. An overview of the top two or three approaches would suffice.
You say "our deeds". What are our deeds?  

My nose is mine but I did not create it because God created all things. I inherited my D.N.A. which made my nose. So things become ours not because we create them but because we are given them. We inherit our nurture and nature 


they make us who we are
we don't choose them.



  1 Pet 4v5 we give back[apodo] an account of the life He first gave us.  


If I give an account of the 1st World War that does not make me responsible for it.  So far I have been describing a Determinist way of reading the Bible in which there is no free will and no human responsibility. 


A chair does not have to make itself to be a chair. We choose. We
choose on the basis of who we are. We do not choose who we are.
Choose you this day whom you will serve is a choice which we will
make solely on the basis on how God first made us.   


On the other hand the Libertarian view is that Adam disobeyed God only because he had the free will to do so, and all human behaviour is down to free will. Here we need to think about whether God's Laws are given to be obeyed or to prove that we can't.
Compatibilism says that Determinism {God is sovereign} is compatible with free will.
Pelagius was a Libertarian and Augustine inclined towards determinism I understand. So these positions have been under scrutiny for a long time. Responsibility has two aspects:  


Instrumental.e.g. who betrayed Jesus? Judas or someone else? Who did
it?
Ultimate responsibility. Why did Judas betray Jesus? Was it because
he had free will or because this destiny was given him by God who
determined his actions?

Luke 22:22 says Jesus went as it was determined but "woe unto that man" that betrayed Him. This means that Judas would be punished even though his actions were determined for him.
We are instrumentally responsible for all our deeds. If I sit in a chair I have done it.
But that does not make me ultimately responsible if God decided before it happened that He would make me do that. So two sorts of responsibility exist and in my experience of Christianity these are frequently treated as one.  I am not sure your question strictly defines in which sense you use the word.