Gay and Kirby introduced trisections, which describe any closed, oriented, smooth 4-manifold X as a union of three 4-dimensional handlebodies. A trisection is encoded in a diagram, namely three collections of curves in a closed oriented surface S , guiding the gluing of the handlebodies. Any morphism f from the fundamental group of X to a finitely generated free abelian group induces a morphism on the fundamental group of S . We express the twisted homology and Reidemeister torsion of (X;f) in terms of the first homology of (S;f) and the three subspaces generated by the collections of curves. We also express the intersection form of (X;f) in terms of the intersection form of (S;f).