The addition or subtraction of a photon from a Gaussian state of light is a versatile and experimentally feasible procedure to create non-Gaussian states. In multimode setups, these states manifest a wide range of phenomena when the photon is added or subtracted in a mode-tunable way. In this paper we derive the truncated correlations, which are multimode generalizations of cumulants, between quadratures in different modes as statistical signatures of these states. These correlations are then used to obtain the full multimode Wigner function, the properties of which are subsequently studied. In particular we investigate the effect of impurity in the subtraction or addition process and evaluate its impact on the negativity of the Wigner function. Finally, we elaborate on the generation of inherent entanglement through subtraction or addition of a photon from a pure squeezed vacuum.