Three new mixed metal selenium oxides materials, Bi2(SeO3)2(SeO4), Bi2(TeO3)2(SeO4), and Bi(SeO3)(HSeO3), have been synthesized by hydrothermal and solid-state reactions using Bi(NO3)3·5H2O, SeO2 (or TeO2), H2SeO4, and Bi2O3 as reagents. The reported materials have been structurally characterized by single crystal X-ray diffraction. While Bi2(SeO3)2(SeO4) and Bi2(TeO3)2(SeO4) are crystallographically centrosymmetric (CS), Bi(SeO3)(HSeO3) crystallizes in a noncentrosymmetric (NCS) space group. The isostructural Bi2(SeO3)2(SeO4) and Bi2(TeO3)2(SeO4) exhibit three-dimensional framework structures that are composed of BiO6, Se(4+)O3 (or Te(4+)O3), and Se(6+)O4 polyhedra. However, Bi(SeO3)(HSeO3) exhibits corrugated layers that are composed of BiO5, Se(4+)O3, and Se(4+)O2(OH) polyhedra. All three materials contain local asymmetric coordination environments attributable to the lone pairs on the Bi(3+), Se(4+), and/or Te(4+) 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 α-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.