Let G be an oriented graph with n vertices and m arcs having underlying graph G. The skew matrix of G is a (–1, 0, 1)-skew-symmetric matrix. The skew eigenvalues of G are the eigenvalues of the skew matrix, and its characteristic polynomial is the skew characteristic polynomial of G. The sum of the absolute values of the skew eigenvalues is the skew energy of G. In this talk, we talk about the skew characteristic polynomial and skew eigenvalues of the joined union of oriented graphs and some of its variations. We show that the skew eigenvalues of the joined union of oriented graphs and some variations of oriented graphs are the union of the skew eigenvalues of the component-oriented graphs except for some eigenvalues, which are given by an auxiliary matrix associated with the joined union. We present concrete examples and explore the links between the polynomials of such operations on oriented graphs and graph neural networks with a focus on combinatorial optimization and natural language processing.