A major focus of experimental interest in Sr2IrO4 has been to clarify how the magnetic excitations of this strongly spin-orbit coupled system differ from the predictions of anisotropic 2D spin-1/2 Heisenberg model and to explore the extent to which strong spin-orbit coupling affects the magnetic properties of iridates. Here, we present a high-resolution inelastic light (Raman) scattering study of the low energy magnetic excitation spectrum of Sr2IrO4 and doped Eu-doped Sr2IrO4 as functions of both temperature and applied magnetic field. We show that the high-field (H>1.5 T) in-plane spin dynamics of Sr2IrO4 are isotropic and governed by the interplay between the applied field and the small in-plane ferromagnetic spin components induced by the Dzyaloshinskii-Moriya interaction. However, the spin dynamics of Sr2IrO4 at lower fields (H<1.5 T) exhibit important effects associated with interlayer coupling and in-plane anisotropy, including a spin-flop transition at Hc in Sr2IrO4 that occurs either discontinuously or via a continuous rotation of the spins, depending upon the in-plane orientation of the applied field. These results show that in-plane anisotropy and interlayer coupling effects play important roles in the low-field magnetic and dynamical properties of Sr2IrO4.