The purpose of this paper is to contribute to the further study of Loday algebroids by introducing, first, the concept of action Loday algebroid and clarifying the notion of a (co)morphism of Loday algebroids. We then focus on the study of Loday algebroids nonlinear connections and their related theory of characteristic classes. These classes arise from multidifferential operators (on the module of smooth sections of the Loday algebroid) in the Loday algebroid cohomology. In particular, the Chern-Simons differential operators for nonlinear connections on Loday algebroids are considered and a generalized Chern- Simons formula for such connections is established. Using representations of Loday algebroids, we define their secondary characteristic classes.