In this paper, a framework of multi-energy system (MES) integrating with a liquid air energy storage (LAES) system was proposed. LAES, where liquid air works as an energy storage media, is a powerful and eco-friendly technology for storing renewable energy resources and reducing grid curtailment. Considering the characteristics of LAES (i.e. cold and heat circulation), the incorporation of LAES system into the Combined Cooling, Heating and Power system can achieve integrated use of energy and effectively save energy. Moreover, the prices of electricity will affect the overall cost of the MES. In other words, the decision-makers of the MES need to consider the uncertainty of electricity prices when making power dispatching decisions. To model the uncertainty of electricity prices, the information gap decision theory method was used to study power dispatching strategies of the MES. Three different strategies were proposed, including risk-neutral, risk-averse and risk-taker. In addition, demand response algorithms were used to study load transfer strategies. The results show that the demand responses of the three strategies are effective in terms of load transfer and cost saving. The total operation cost in the risk-neutral strategy with demand response can be 6.82% less than that without demand response; In the risk-taker strategy with demand response, the allowable grid electricity price is reduced by 25.24% when the opportunity cost drops by $8,000, and 23.32% without demand response. With additional robustness cost, the acceptable price change ratio using demand response is 21.91% in the risk-averse strategy, and 20.04% without demand response.