Five novel coordination polymers [Zn₂(OA)(4,4′-bipy)(H₂O)]·0.5(4,4′-bipy) (1), [Zn₂(OA)(dib)(H₂O)]·H₂O (2), [Zn₂(OA)(bbi)₂]·3H₂O (3), [Zn₂(OA)(phen)₂(H₂O)] (4) and [Zn₄(OA)₂(2,2′-bipy)₂(H₂O)]·2H₂O (5) were obtained by hydrothermal reactions of Zn(NO₃)₂·6H₂O with a V-shaped multicarboxylate ligand 3,3′,4,4′-oxydiphthalic acid (H₄OA) and a series of N-donor ligands, namely 4,4′-bipyridine (4,4′-bipy), 1,4-di(1-imidazolyl)benzene (dib), 1,1′-(1,4-butanediyl)bis(imidazole) (bbi), 1,10-phenanthroline (phen), 2,2′-bipyridine (2,2′-bipy). The structures of the complexes were established by single-crystal X-ray diffraction analysis. Complex 1 exhibits a robust 3D porous structure with uncoordinated 4,4′-bipy molecules filling the cavities. Complexes 2 and 5 show a complicated 3D framework, while complexes 3 and 4 have a 2D network and a 1D helical chain structure, respectively. The results indicate that the multicarboxylate OA⁴⁻ ligand can adopt varied coordination modes in the formation of the complexes and the influence of the N-donor ligand on the structure of the complexes is discussed. The photoluminescence properties of H₄OA and 1–5 were studied in the solid state at room temperature. Moreover, nonlinear optical measurements showed that 5 displayed a second-harmonic-generation (SHG) response of 0.5 times of that for urea. The results suggested that the configuration and flexibility of the ligands play a key role in directing the related properties of the complexes.