This dissertation is comprised of four completed papers and one additional chapter, all of which share the common themes of oscillations, magnetic fields, and superfluidity-superconductivity of neutron stars. Each of these subjects is first reviewed, and connected to the individual chapters where appropriate. The calculation of the p-and g-modes of a superfluid neutron star with leptonic buoyancy is then explained. This is followed by the description of a relativistic multifluid hydrodynamics formulation relevant for finite-temperature superfluid neutron star cores threaded by proton flux tubes and neutron vortex lines. Next the gravitational radiation-unstable modes of Riemann ellipsoids are computed using the tensor-virial method for a model hypermassive neutron star. The final chapters discuss the magnetohydrodynamic (MHD) stability of magnetars threaded by extremely strong magnetic fields, first inside the core where ideal MHD is applicable, and then in the crust where a Hall MHD prescription is required.