The progressing development of Internet of Things (IoT) has accelerated the emergence of resource-intensive and latency-sensitive mobile applications, which throws out a great challenge to the battery-powered wireless devices (WDs) with low-computing capabilities. To solve this intractable issue, we investigate an intelligent reflecting surface (IRS)-assisted multiantenna wireless-powered mobile edge computing (WP-MEC) system, in which WDs first harvest wireless energy emitted by a hybrid access point (HAP), then offload their tasks to the edge server, and finally download the results. In consideration of the practical scenarios, the finite computing capability of edge server and the nonlinear end-to-end power conversion of energy harvesting (EH) circuits at WDs are considered. In addition, an IRS is deployed to improve the efficiency of wireless power transfer (WPT) and the rate of data transmission between HAP and WDs. Under this setup, both space division multiple access (SDMA) and time division multiple access (TDMA) protocols are exploited and evaluated for data transmission. For each protocol, we maximize the computational rate by jointly optimizing time allocation, beamforming designs of HAP and IRS, as well as offloading strategies of WDs. To solve the problem formulated under the SDMA protocol, we propose an efficient alternating optimization (AO) algorithm. For the problem under the TDMA protocol, an AO algorithm with low complexity is proposed. Numerical results demonstrate the high effectiveness of the proposed algorithms and the superiority of the SDMA protocol over the TDMA protocol.