We study the effects of rapid temperature and magnetic field changes on the nonequilibrium relaxation dynamics of magnetic vortex lines in disordered type-II superconductors by employing an elastic line model and performing Langevin molecular dynamics simulations. In a previously equilibrated system, either the temperature is suddenly changed or the magnetic field is instantaneously altered which is reflected in adding or removing flux lines to or from the system. The subsequent aging properties are investigated in samples with either randomly distributed pointlike or extended columnar defects, which allows us to distinguish the complex relaxation features that result from either type of pinning centers. One-time observables such as the radius of gyration and the fraction of pinned line elements are employed to characterize steady-state properties, and two-time correlation functions such as the vortex line height autocorrelations and their mean-square displacement are analyzed to study the nonlinear stochastic relaxation dynamics in the aging regime.