Understanding the dynamics of gels at soft interfaces is vital for a range of applications, from biocatalysis and drug delivery to enhanced oil recovery applications. Herein, we use dissipative particle dynamics simulations to focus on the shape changes of a cubic nanogel as it adsorbs from the aqueous phase onto the oil-water interface, effectively acting as a compatibilizer. Upon adsorption at the interface, the hydrogel spreads over the interface, adopting various shapes depending on its size and cross-link density. We characterize these shapes by the shape anisotropy and an effective extent of spreading. We highlight the differences between these characteristics for cubic and spherical nanogels and show that the choice of the cubic shape over the spherical one results in a wider range of topographies that could be dynamically prescribed onto the soft interface due to the gels' adsorption. We first validate our model parameters with respect to the known experimental values for polyacrylamide (PAAm) gels and focus on spreading and shape changes of PAAm nanogels onto the oil-water interfaces. We then probe the behavior of active gels by changing an affinity of the polymer matrix for the solvent, which can be caused by the application of an external stimulus (light, temperature, or change in the chemical composition of solvent). Furthermore, we focus on the interactions between multiple gels placed at the liquid-liquid interface. We show that controlling the shapes and the clustering of the gels at the interfaces via variations in solvent quality result in tailoring the dynamics and topography of soft nanostructured interfaces. Hence, our findings provide insights into the design of soft active nanostructured interfaces with topographies controlled externally via solvent quality.