Weyl semimetals in a magnetic field give rise to interesting nonlocal electronic orbits: the ballistic transport through the bulk enabled by the chiral Landau levels is combined with a momentum-space sliding along the surface Fermi-arc driven by the Lorentz force. Bulk chiral Landau levels can also be induced by axial fields whose sign depends on the chirality of the Weyl point. However, the microscopic perturbations that give rise to them can be described in terms of gauge fields only in the low-energy sectors around the Weyl points. In addition, since pseudofields are intrinsic, there is no apparent reason for a Lorentz force that causes sliding along the Fermi arcs. Therefore, the existence of nonlocal orbits driven exclusively by pseudofields is not obvious. Here we show that for systems with at least four Weyl points in the bulk spectrum, nonlocal orbits can be induced by axial fields alone. We discuss the underlying mechanisms by a combination of analytical semiclassical theory, the microscopic numerical study of wave-packet dynamics, and a surface Green's function analysis.