Blockchain-based peer-to-peer ET (P2P-ET) is expected to be a key element of the next-generation power system due to its decentralized nature, immutable data structure and smart contract capability that allows energy contracts to be made on the blockchain. However, blockchain suffers from performance, scalability and privacy challenges. To address these challenges, we propose MuLCOff, a multi-layer consensus and off-chain computation-based P2P-ET system. MuLCOff's architecture consists of three network layers, where each layer consists of multiple blockchain network shards that can operate as an independent permissioned blockchain network. The network shards can participate in multiple layers of consensus simultaneously. Unlike previous systems, MuLCOff supports the concurrent processing of transactions across different consensus layers. Each network shard also has an associated off-chain infrastructure, which allows performing heavy computations and private energy negotiation outside the blockchain. Experimental results indicate that the proposed multi-layer consensus provides 87% better throughput compared to state of the art consensus algorithms. Moreover, MuLCOff's off-chain-based ET scheme reduces the latency by 75 to 124 times and the computation cost by a factor of 80 to 94.6 respectively compared to its on-chain counterpart.