The application of intelligent reflecting surface (IRS) into wireless powered mobile edge computing (WP-MEC) systems is investigated, where both time division multiple access (TDMA) and non-orthogonal multiple access (NOMA) schemes are considered for uplink (UL) offloading. We propose three different dynamic IRS beamforming (DIBF) 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 TDMA and NOMA schemes, respectively, by jointly optimizing the IRS BF and the resource allocation. An analytical comparison for the computation rate of TDMA and NOMA-based UL offloading schemes is provided. Finally, we propose computationally efficient algorithms to solve the corresponding computation rate maximization problems under the proposed DIBF framework. Numerical results unveil that the optimal time allocated to DL WPT can be effectively reduced with the aid of IRSs, which is beneficial for both the system's spectral efficiency and energy efficiency.