Chiral multiferroic langasites have attracted attention due to their doubly chiral magnetic ground state within an enantiomorphic crystal. We report on a detailed resonant soft x-ray diffraction study of the multiferroic Ba₃TaFe₃Si₂O₁₄ at the Fe L_2,3 and oxygen K edges. Below T_N (≈27K) we observe the satellite reflections (0,0,τ), (0,0,2τ), (0,0,3τ), and (0,0,1-3τ) where τ ≈ 0.140 ± 0.001. The dependence of the scattering intensity on x-ray polarization and azimuthal angle indicate that the odd harmonics are dominated by the out-of-plane (ĉ axis) magnetic dipole while the (0,0,2τ) originates from the electron density distortions accompanying magnetic order. We observe dissimilar energy dependencies of the diffraction intensity of the purely magnetic odd-harmonic satellites at the Fe L₃ edge. Utilizing first-principles calculations, we show that this is a consequence of the loss of threefold crystal symmetry in the multiferroic phase.