The motions of domain walls driven by magnetic field in soft magnetic nanostripes were calculated. The domain walls reveal steady motions in the low fields and oscillations of their internal structure above a critical field. A developed soliton model of the walls explains its dynamics by the motions of a limited number of magnetic topological solitons such as vortex and antivortex. We predict the reduced wall velocity and critical field in the low-field regime, and increased wall-oscillation frequency in nanostripes, compared to 1D Walker solution for bulk magnets. The critical field and velocity are determined by the nanostripe sizes, whereas the oscillation frequency depends only on the field strength.