How does the 51 percent or 2/3 majority voting rule work? For a block to be added to the chain, it needs vote from majority of miners, is that correct? If yes, does that mean a single block gets worked upon by all of the miners?
For a block to be added to the chain, it needs vote from majority of miners, is that correct? If yes, does that mean a single block gets worked upon by all of the miners?


There is no voting. Each miner works on their own version of blocks. Once they have found the hash of the block header which meets the difficulty target, they broadcast the block to the rest of the network. When the other full nodes and miners receive this block, they will first verify if the block meets all the protocol rules, and the transactions within the block are also valid. The bitcoin software is designed so as to accept the chain with the most proof of work. In most cases this is also same as the longest chain. So, when the new block is received by the nodes, they would add this block on top of the existing chain if the block is valid. When the block is received, the other miners would see that they have lost the 'race' for that particular block height. Now they will start working on the next block, by building on the top of the block that they just received.


  How does the 51 percent or 2/3 majority voting rule work?


I assume you are referring to 51% attack. 51% attack basically means that if a miner has more than 50% of the hash power of the total network, he has higher probability of mining blocks that is faster than the rest of the network combined. If that is the case, then the miner can double spend the bitcoins. If you want more clarity as to what 51% attack is, then you can refer here. Regarding 2/3rd voting, you might have read that as a part of Byzantine Fault Tolerance (BFT) threshold. However, bitcoin doesn't exist within the normal model of BFT consensus. Under conventional assumptions bitcoin will converge on a stable history if honest participants have a majority hashpower (>50%).