Power-to-gas is an emerging energy conversion technology. When integrating power-to-gas into the combined cooling, heating and power system, renewable generations can be further accommodated to synthesize natural gas, and additional revenues can be obtained by reutilizing and selling the synthesized gas. Therefore, it is necessary to address the optimal operation issue of the integrated system (Combined cooling, heating and power-Power-to-gas) for bringing the potential benefits, and thus promoting energy transition. This paper proposes a Wasserstein and multivariate linear affine based distributionally robust optimization model for the above issue considering multiple uncertainties. Specifically, the uncertain distribution of wind power and electric, thermal, cooling loads is modeled as an ambiguity set by applying the Wasserstein metric. Then, based on the ambiguity set, the proposed model with two-stage structure is established. In the first-stage, system operation cost (involving the energy exchange and carbon emission costs, etc.) is minimized under the forecast information. In the second stage, for resisting the interference of multiple uncertainties, the multivariate linear affine policy models are constructed for operation rescheduling under the worst-case distribution within the ambiguity set, which is capable of adjusting flexible resources according to various random factors simultaneously. Simulations are implemented and verify that: 1) both the economic and environmental benefits of system operation are improved by integrating power-to-gas; 2) the proposed model keeps both the conservativeness and computational complexity at low levels, and its solutions enable the effective system operation in terms of cost saving, emission reduction, uncertainty resistance and renewable energy accommodation.