Multidimensional upwind residual distribution schemes are applied to the eight-wave equations of ideal magnetohydrodynamics. These schemes extend the high-resolution upwind finite volume methodology to a truly multidimensional finite element context on unstructured grids. Both first-and second-order linear and second-order nonlinear monotonicity preserving schemes are discussed. An approximate conservative linearization technique is derived for general hyperbolic systems together with a conservative correction technique, which guarantees the full conservation of the convective fluxes. The solenoidal condition of the magnetic field is enforced by Powell's source term approach. Both implicit and explicit time-integration strategies have been implemented. The spatial accuracy and the shock-capturing properties of the schemes in the steady state are investigated numerically. Computational results are presented for a bow shock over a cylinder and for a supermagnetosonic flow in a channel.