In this letter, we consider a multi-server mobile edge computing (MEC) network where a user with limited computation ability aims to complete an intensive computation task in a short time under the help of multiple edge servers. We study the delay-minimization offloading schemes with and without user’s energy constraint, which involve the joint optimization of task allocation ratio for local computation, the wireless offloading manner (i.e., non-orthogonal multiple access (NOMA) offloading or single-server offloading mode), and the server pair selection. Specifically, the joint optimal solutions are derived in semi-closed forms and the critical conditions of switching offloading manners are derived in closed form. Numerical results corroborate the superiority of our proposed offloading scheme in terms of overall latency under various settings.