The fluid seepage in oil reservoir-type gas storage involves three phases of oil, gas, and water. The storage capacity not only includes the pore space for gas displacement of liquid, but involves dissolution and component mass transfer between oil and gas. To elucidate the relative permeability characteristics of multiphase displacement among oil, gas, and water and the composition of the gas storage space during cyclic injection and production, multiple cycles of gas-water, oil-water, and gas-oil multiphase displacement and relative permeability experiments were conducted, along with long-core physical simulation experiments under multi-cycle injection and production, based on the operational parameters of reservoir-type gas storage. The seepage patterns of two-phase mutual displacement, gas displacing fluid efficiencies, and fluid saturation changes during cyclic injection and production, and the changes in oil and gas phase states were analyzed. Furthermore, the variations in seepage capacity, oil displacement efficiency, and storage space during cyclic injection and production were investigated. The experimental result showed that: (1) during the processes of multi-cycle two-phase mutual displacement, the water phase reduced the seepage capacity of the gas phase and oil phase, which was unfavorable for the construction and expansion of gas storage facilities. The gas-oil mutual displacement process reduced the residual oil saturation and increased the volume of mobile fluid, which was conducive to the construction and expansion of gas storage facilities. (2) The physical simulation of long-core reservoir construction was performed using the approach of “gas displacement to ultimate recovery under formation pressure + cyclic injection and production within upper and lower pressure limits”. The model’s final oil displacement efficiency reached 65.11%, with 20% from water displacement, 37.51% from gas displacement, and 7.6% from cyclic injection and production. The continuous gas displacement stage was the primary recovery enhancement stage, while the cyclic injection-production stage served as the reservoir construction stage. (3) The pore volume displaced by gas in long-core experiments constituted the main part of the storage capacity, accounting for more than 70%, while the pore volume of solution gas in residual oil and residual oil shrinkage accounted for less than 30%. The storage capacity and working gas volume tended to stabilize after the 14th injection-production cycle, primarily influenced by the gas saturation. Therefore, it is recommended that in the construction of reservoir-type gas storage, premature depletion-driven gas production should be avoided. Instead, a “recovery enhancement” strategy should be prioritized before “reservoir construction”. Reservoir pressure during gas-oil displacement should be maintained until the ultimate recovery efficiency is achieved, after which cyclic injection and production can be implemented to construct the reservoir. This can adequately increase oil and water recovery degree, thereby increasing the storage capacity and working gas volume.