In this paper we discuss how certain algebraic invariants of 3-manifolds can be effectively used in the study of fiberedness and the Thurston norm of links. In particular we use twisted Alexander polynomials to prove that the exterior of a certain graph knot, whose splice diagram is given, is not fibered. Then we consider three 2-component graph links built out of this knot. For these links we use the same technique, involving twisted Alexander polynomials to discuss their fiberedness and Turston norm. This allows us to demonstrate the effectiveness of twisted Alexander polynomials in this context (links in homology spheres different from S³), where no calculations exist in the literature.