Compact objects in a binary system can accrete matter through an accretion disk. In the case of neutron stars with strong magnetic fields, the accretion disk terminates at a particular radius and the matter is channeled along the magnetic field lines. For a dipolar magnetic field, this causes the matter to be accreted to the poles of the neutron star through an accretion funnel. We use magnetohydrodynamics and a variable adiabatic index Equation of State to study the accretion funnel region of strongly-magnetized neutron stars. Previous works in this domain focused on neutron stars with aligned magnetic and rotation axes. However, most of the detected neutron stars have some degree of misalignment between these axes, making their study important. In this work, we obtain self-consistent accretion solutions for strongly-magnetized misaligned neutron stars by considering bremsstrahlung and cyclosynchrotron emission as well as shocks.