Oscillating grid turbulence (OGT) is a specific situation allowing to investigate the equilibrium between the turbulent kinetic energy, k, and the dissipation rate, ε, without any mean flow. One of its main features is that, in homogeneous fluids, the turbulence intensity decreases with the distance to the vibrating grid used to generate the forcing. OGT is thus usually described in terms of depth profiles of turbulent quantities. In this paper, we discuss experiments realized in two different setups and compare our results for all turbulent quantities with past studies. The results on the turbulent kinetic energy and the integral length scale lead us to propose a parametric model for the eddy viscosity, νt, taking into account the spatial decay of the turbulence being slightly different than previous descriptions. Indeed, we find that νt is best described as a constant value over a certain depth, Hs, before decreasing quickly as a power law in z^−3/2 . The specific depth Hs is defined at the depth where a discontinuity of the integral length scale is observed. Physically, it corresponds to the depth at which the presence of the grid no longer influences the flow. We also describe OGT in the case of a two-layer fluid. The description of the turbulence at depths z far from the position of the interface h (0 < z/h < 0.6) is very similar to the case of an homogeneous fluid, whereas the region near the interface (0.6 < z/h < 1) is strongly altered by the presence of the fluid boundary. Surprisingly, νt (at the difference of the others turbulent quantities) no longer depends on z in such configuration. Finally, we investigate mixing processes at the interface in this context. Thanks to large field measurement (about the width of the tank), we were able to identify large scale coherent structures as well as the turbulent flow. We discuss the entrainment law of the interface, and its relationship with the Richardson number based on different definitions used in previous studies, as well as by using our observations of the turbulent flow properties at the interface. Our observations suggest that mixing at the interface in OGT is controlled by the turbulent flow properties at the interface but could also be influenced by weak mean flow features, this could explain the difficulty to discriminate a simple dependency of the entrainment rate with the Richardson number.