Three new mixed metal selenium oxides materials, Bi-2(SeO3)(2)(SeO4), Bi-2(TeO3)(2)(SeO4), and Bi(SeO3)(HSeO3), have been synthesized by hydrothermal and solid-state reactions using Bi(NO3)(3)center dot 5H(2)O, SeO2 (or TeO2), H2SeO4, and Bi2O3 as reagents. The reported materials have been structurally characterized by single crystal X-ray diffraction. While Bi-2(SeO3)(2)(SeO4) and Bi-2(TeO3)(2)(SeO4) are crystallographically centrosymmetric (CS), Bi(SeO3)(HSeO3) crystallizes in a noncentrosymmetric (NCS) space group. The isostructural Bi-2(SeO3)(2)(SeO4) and Bi-2(TeO3)(2)(SeO4) exhibit three-dimensional framework structures that are composed of BiO6, Se4+O3 (or Te4+O3), and Se6+O4 polyhedra. However, Bi(SeO3)(HSeO3) exhibits corrugated layers that are composed of BiO5, Se4+O3, and Se4+O2(OH) polyhedra. All three materials contain local asymmetric coordination environments attributable to the lone pairs on the Bi3+, Se4+, and/or Te4+ cations. Powder second-harmonic generation (SHG) measurements on NCS Bi(SeO3)(HSeO3) using 1064 nm radiation indicate that the material has a SHG efficiency of approximately 20 times that of alpha-SiO2 and is not phase-matchable (type 1). The origin and magnitude of the SHG efficiency of Bi(SeO3)(HSeO3) is explained by determining the net direction of the polarizations arising from individual asymmetric polyhedra. Infrared spectroscopy, thermal analysis, elemental analysis, and dipole moment calculations for the reported materials are also presented.