Underground salt cavern storage has become the preferred medium for storing gas energy and strategic substances. Salt caverns are suitable for storing small molecular gases due to the low porosity and permeability of salt rocks. This paper comprehensively analyzes the physical properties of four gases - hydrogen, helium, methane, and carbon dioxide - under subsurface temperature and pressure conditions. It categorizes the flow regimes of these gases in salt rocks under geological pressure conditions based on the Knudsen number. In a typical 1000 m salt cavern, the predominant permeation flow regime of four gases in the surrounding rock is Klinkenberg flow, with helium potentially undergoing transitional flow at low operation pressures. A 3D numerical model is established for an actual salt cavern to compare the permeation and leakage characteristics of these gases within salt rock formations. Results indicate that, under identical operation conditions, the permeation range of the gases decreases in the following order: hydrogen > methane > helium > carbon dioxide. Under the cyclic operation pressures, the cumulative leakage amount of hydrogen, helium, and methane increases over time, while that of carbon dioxide initially rises and then decreases. This behavior is attributed to the fact that the reverse-permeation rate of carbon dioxide at low pressures exceeds its permeation rate at high pressures. Over 30 years cyclic operation, the leakage ratios of the gases are as follows: hydrogen (13.29 %), methane (9.34 %), helium (7.47 %), and carbon dioxide (0.93 %), with hydrogen exhibiting the highest and carbon dioxide the lowest leakage ratios. Larger permeability results in a larger permeation range, while larger porosity leads to a smaller permeation range. When the permeability of salt layer is greater than 1e-20 m2, the permeation range of hydrogen significantly increases. Gas leakage ratios increase with permeability nonlinearly and increase with porosity linearly. The impact of salt layer permeability on leakage ratios is greater than that of porosity. This study provides crucial guidance for the selection of geological formations for storing hydrogen, helium, methane, and carbon dioxide in salt caverns, as well as the investigation of gas permeation characteristics in salt layers.