We investigate nonlocal vortex motion in weakly pinning a-NbGe nanostructures, which is driven by a transport current I and remotely detected as a nonlocal voltage Vnl. At high I, the measured Vnl exhibits dramatic sign reversals that at low and high temperatures T occur for opposite polarities of I. The sign of Vnl becomes independent of that of the drive current at large abs(I). These unusual effects can be nearly quantitatively explained by a novel enhancement of magnetization, arising from a nonequilibrium distribution of quasiparticles at high T, and a Nernst-like effect resulting from local electron heating at low T.