We report the preparation and characterization of cross-linked ionogels (x-IGs) composed of polyethylene glycol diacrylate (PEGDA) and the protic ionic liquid, ethylammonium nitrate (EAN). The cross-linking process has a huge effect on the mechanical properties of the solutions (forming stiff solids from Newtonian solutions) and a minimum penalty on the ionic conductivity. The interdependence of the mechanical and dielectric properties with the network structure of the x-IGs was studied using three experimental probes: torsion and compression mechanical testing, dielectric spectroscopy and small angle neutron scattering. The microstructure, the mechanical strength and the conductivity of the x-IGs depend strongly on the polymer concentration and weakly on the temperature. High modulus and relatively low conductivities are associated to small cross-link junction lengths, xi, observed in concentrated samples, whereas large xi values, observed in dilute samples, result in high conductivities and relatively low modulus. The topological restriction to ionic transport (i.e., to conductivity) is quantified by the obstruction factor, which increases monotonically with xi, while the shear modulus exhibits a power law behavior, G similar to xi(-3), in accordance to linear viscoelastic theory.