The coincidence of high levels of variable, non-dispatchable generation from renewable energy sources (RESs) and congested electricity networks imposes significant constraint payments (CP) on electricity system operators (ESOs) which ultimately is charged to the customers. This paper is inspired by this challenge and proposes an integrated electricity, gas, and transportation energy system taking advantage of power-to-gas (P2G) facilities and electricity/gas storage devices to enhance operational efficiency. It proposes mobile gas storage systems (MGSs) that can store and carry liquid hydrogen or liquefied natural gas (LNG) to the load points or remote locations without access to the gas network. So, the green energy of RESs in the form of gases can be injected, transported, and reutilized in the natural gas network or stored in MGS facilities. Besides, the mobile electricity storage system (MES) can directly store the redundant electricity produced by RESs, and the railway transportation system carries both the MESs and MGSs to the load point of electrical and gas systems. The proposed model reflects CP to wind in the marketing phase and considers incentives for the hydrogen-burning generators. Also, a stochastic platform is employed to capture the inherent uncertainties in the predicted values of the load and RESs’ generation. The model is formulated as a mixed-integer second-order cone programming problem and tested on an IEEE 118-bus system integrated with a 14-node gas network and a railway system. The result shows that employing the multi-vector energy system (MVES) elements reduces the total operational cost by 47%, and the CP to wind is reduced by 99.8% by absorbing almost the whole green energy of wind farms while relieving congestion in the electrical grid.