We perform a theoretical and computational study of the hydrogen atom and hydrogenlike ions Ne9+ and Ar17+ subject to strong pulses of linearly-polarized electromagnetic fields. To solve the problem, we apply the generalized pseudospectral method for the Dirac equation in spherical coordinates and suggest a transformation of the Hamiltonian that removes the spurious eigenstates. The ionization probabilities are calculated for several peak field strengths both within and beyond the dipole approximation. We compare the ionization probabilities for these hydrogenlike systems subject to the external fields with the appropriately scaled parameters, so the nonrelativistic treatment in the dipole approximation returns identical results for all three targets. We identify the field strength regions where the relativistic and nondipole effects become important. To assess the applicability of the dipole approximation, we calculate the Lorentz deflection parameter proposed previously to estimate the nondipole effects due to the influence of the magnetic component of the external electromagnetic field. Based on our present results, we find that the dipole approximation works well if this parameter is of the order of 10-3 or less.