Torsion in a ribbon geometry produces longitudinal stresses varying across the ribbon width, giving rise to significant second-order elastic, plastic and magnetoelastic effects. An overall agreement between the experimental curves for torque-torsion angle and inverse Wiedemann effect and theoretical predictions has been found for both as-quenched and for torsionally stress-annealed ribbons. Annealed ribbons exhibit tremendous elastic and magnetic anisotropies which can be easily controlled by varying the dimensions of the cross-section as well as the stress annealing conditions.