This paper considers a multi-functional orthogonal frequency division multiplexing (OFDM) system with integrated sensing, communication, and powering (ISCAP), in which a multi-antenna base station (BS) transmits OFDM signals to simultaneously deliver information to multiple information receivers (IRs), provide energy supply to multiple energy receivers (ERs), and sense potential targets based on the echo signals. To facilitate ISCAP, the BS employs the joint transmit beamforming design by sending dedicated sensing/energy beams jointly with information beams. Furthermore, we consider the beam scanning for sensing, in which the joint beams scan in different directions over time to sense potential targets. In order to ensure the sensing beam scanning performance and meet the communication and powering requirements, it is essential to properly schedule IRs and ERs and design the resource allocation over time, frequency, and space. More specifically, we optimize the joint transmit beamforming over multiple OFDM symbols and subcarriers, with the objective of minimizing the average beampattern matching error of beam scanning for sensing, subject to the constraints on the average communication rates at IRs and the average harvested power at ERs. We find converged high-quality solutions to the formulated problem by proposing efficient iterative algorithms based on advanced optimization techniques. We also develop various heuristic designs based on the principles of zero-forcing (ZF) beamforming, round-robin user scheduling, and time switching, respectively. Numerical results show that our proposed algorithms adaptively generate information and sensing/energy beams at each time-frequency slot to match the scheduled IRs/ERs with the desired scanning beam, significantly outperforming the heuristic designs.