An intelligent reflecting surface (IRS)-aided wireless powered mobile edge computing (WP-MEC) system is conceived, where each device's computational task can be divided into two parts for local computing and offloading to mobile edge computing (MEC) servers, respectively. Both time division multiple access (TDMA) and non-orthogonal multiple access (NOMA) schemes are considered for uplink (UL) offloading. Given the capability of IRSs in intelligently reconfiguring wireless channels over time, it is fundamentally unknown which multiple access scheme is superior for MEC UL offloading. To answer this question, we first investigate the impact of three different dynamic IRS beamforming (DIBF) schemes on the computation rate of both offloading schemes, based on the flexibility for the IRS in adjusting its beamforming (BF) vector in each transmission frame. Under the DIBF framework, computation rate maximization problems are formulated for both the NOMA and TDMA schemes, respectively, by jointly optimizing the IRS passive BF and the resource allocation. We rigorously prove that offloading adopting TDMA can achieve the same computation rate as that of NOMA, when all the devices share the same IRS BF vector during the UL offloading. By contrast, offloading exploiting TDMA outperforms NOMA, when the IRS BF vector can be flexibly adapted for UL offloading. Despite the non-convexity of the computation rate maximization problems for each DIBF scheme associated with highly coupled optimization variables, we conceive computationally efficient algorithms by invoking alternating optimization. Our numerical results demonstrate the significant performance gains achieved by the proposed designs over various benchmark schemes.