This paper considers intelligent reflecting surface (IRS)-aided simultaneous wireless information and power transfer (SWIPT) in a multi-user multiple-input single-output (MISO) interference channel (IFC), where multiple transmitters (Txs) serve their corresponding receivers (Rxs) in a shared spectrum with the aid of IRSs. Our goal is to maximize the sum rate of the Rxs by jointly optimizing the transmit covariance matrices at the Txs, the phase shifts at the IRSs, and the resource allocation subject to the individual energy harvesting (EH) constraints at the Rxs. Towards this goal and based on the well-known power splitting (PS) and time switching (TS) receiver structures, we consider three practical transmission schemes, namely the IRS-aided hybrid TS-PS scheme, the IRS-aided time-division multiple access (TDMA) scheme, and the IRS-aided TDMA-D scheme. The latter two schemes differ in whether the Txs employ deterministic energy signals known to all the Rxs. Despite the non-convexity of the three optimization problems corresponding to the three transmission schemes, we develop computationally efficient algorithms to address them suboptimally, respectively, by capitalizing on the techniques of alternating optimization (AO) and successive convex approximation (SCA). Moreover, we conceive feasibility checking methods for these problems, based on which the initial points for the proposed algorithms are constructed. Simulation results demonstrate that our proposed IRS-aided schemes significantly outperform their counterparts without IRSs in terms of sum rate and maximum EH requirements that can be satisfied under various setups. In addition, the IRS-aided hybrid TS-PS scheme generally achieves the best sum rate performance among the three proposed IRS-aided schemes, and if not, increasing the number of IRS elements can always accomplish it.