Gate-all-around (GAA) metal-oxide-semiconductor field-effect transistors (MOSFETs) is one of the mainstream research topics of the current era in the field of semiconductor devices since they are the most efficient architectures among all multiple-gate (MG) devices. Incorporating strain in GAA device can boost the device performance significantly. As such, strained-Si (S-Si) GAA MOSFETs can have vast technological importance in future high performance logic technologies. Due to imperfections in the fabrication process, the cross-section of a GAA device may deviate from its ideal circular nature, giving rise to an elliptical structure. Capacitance-Voltage (C-V) characteristics is an important tool for characterizing such devices. For the first time, we analytically model the quasi-static C-V characteristics of elliptical S-Si GAA MOSFETs for various operating regions. We have incorporated quantum mechanical effects (QMEs) which cannot be neglected in devices having ultra-nanometre dimensions. Computations were carried out to investigate the effects of device dimensions, interface trap charges, doping concentration, germanium mole fraction and stress on the C-V characteristics of S-Si GAA MOSFETs. The possibilities for enhancing the device performance by using high-k dielectrics have also been investigated.