We propose an investigation of residual distribution schemes for numerical approximation of two-dimensional hyperbolic systems of conservation laws on general quadrilateral meshes. In comparison to the use of triangular cells, usual basic features are recovered, an extension of the upwinding concept is given, and a Lax-Wendroff type theorem is adapted for consistency. We show how to retrieve many variants of standard first- and second-order accurate schemes. They are proven to satisfy this theorem. An important part of this paper is devoted to the validation of these schemes by various numerical tests for scalar equations and Euler equations for compressible fluid dynamics on non-Cartesian grids. In particular, second-order accuracy is reached by an adaptation of the linearity-preserving property to quadrangle meshes. We discuss several choices as well as the convergence of iterative method to steady state. We also provide examples of schemes that are not constructed from an upwinding principle