Artificial microswimmers have gained significant attention recently for use in biomedical applications, such as drug delivery, and microfluidic applications, such as mixing. The small scale of the swimmers requires external actuation mechanisms, such as magnetic fields. Acoustic actuation, due to its biocompatible nature, can be used alongside magnetic fields to improve swimming performance. Several experimental studies have already shown the propulsion of both non-helical and helical swimmers with acoustic fields. Here, we present a simple model to evaluate the acoustic radiation force on helices. The methodology can be applied to solve for the force on other complicated structures as well, reducing the high computational cost required with other methods, such as the finite-element method. The approach is coupled with a resistive force theory-based model of slender magnetized helices to evaluate the complete three-dimensional trajectories of the swimmers under acoustic and magnetic fields. Traveling waves are shown to reduce swimmer wobbling significantly while also generating a significant push. Standing waves, on the other hand, are observed to place the swimmer in a unique position and orientation, which can be exploited for accurate positioning or micro-mixing.