We study the geodesics of charged black holes in polynomial Maxwell Lagrangians, a subclass of models within the nonlinear electrodynamics (NLED). Specifically, we consider black holes in Kruglov, power-law, and Ayon-Beato-Garcia models. Our exploration on the corresponding null bound states reveals that a photon can orbit the extremal black holes in stable radii outside the corresponding horizon, contrary to the case of the Reissner-Nordstrom black holes. The reason behind this is the well-known theorem that a photon in a NLED background propagates along its own effective geometry. This nonlinearity is able to shift the local minimum of the effective potential away from its corresponding outer horizon. For the null scattering states, we obtain corrections to the weak deflection angle off the black holes. We rule out the power-law model to be physical since its deflection angle does not reduce to the Schwarzschild in the limit of the vanishing charge.