Nonradiating states of light have recently received a lot of attention in nanophotonics owing to their ability to confine and enhance the electromagnetic fields at the nanoscale. Such optical states not only offer a promising way to overcome the problem of losses associated with plasmonic materials, but also constitute an efficient platform for interaction of light and matter. Here, we report the radiationless states in compact, ultrathin transition-metal-dichalcogenide metasurfaces, namely bound states in the continuum (BICs). Through applying the multipole analysis to the BIC-based metasurfaces, we demonstrate that the BICs can be classified as magnetic dipole (MD) and electric toroidal dipole (TD) modes, both of which correspond to the Γ-point symmetry-protected BIC. Due to the large field confinement inside the nanoresonators originating from the BICs, the strong coupling is realized between quasi-BICs and the exciton resonance, showing that the Rabi splitting energy can be up to 134 meV and 162 meV for the MD and TD quasi-BIC, respectively. We reveal that reduction of the effective mode volume is highly responsible for the enhancement of coupling strength. Furthermore, it is demonstrated that a large mode volume can lead to increase of the field leakage, which enables our metasurfaces to find applications in, for instance, label-free sensing based on refractometric detection.