Many magnetic structures in the solar atmosphere evolve rather slowly so that they can be assumed as (quasi-)static or (quasi-)steady and represented via magneto-hydrostatic (MHS) or magneto-hydrodynamic (MHD) equilibria, respectively. While exact 3D solutions would be desired, they are extremely difficult to find in steady MHD. We construct solutions with magnetic and flow vector fields that have three components depending on all three coordinates. We show that the non-canonical transformation method produces quasi-3D solutions of steady MHD by mapping 2D or 2.5D MHS equilibria to strongly related steady-MHD states, displaying highly complex currents. The existence of geometrically complex 3D currents within symmetric field-line structures provide the base for efficient dissipation of the magnetic energy in the solar corona by Ohmic heating. We also discuss the possibility of achieving force-free fields, and find that they only arise under severe restrictions of the field-line geometry and of the magnetic flux density distribution.