Can two different nonces and different blocks produce the same hash? Say, I want to erase the record of a transaction by changing a block. Can I go back to that block and find a new block and nonce combination that makes the same hash? 

Is it a case that finding such a new combination is computationally hard or is it actually impossible?
One of the main properties of a hash algorithm is collision resistance. If you would find an identical hash with two different datasets, then we would speak of a hash collision.

This is extremely unlikely to happen. The mathematical chance that a sha256 collision would happen is smaller then the actual chance that the universe will implode in this moment.

https://crypto.stackexchange.com/questions/24732/probability-of-sha256-collisions-for-certain-amount-of-hashed-values