Hybrid organic-inorganic lead halide perovskites have emerged as promising materials for various applications, including solar cells, light-emitting devices, dielectrics, and optical switches. In this work, we report the synthesis, crystal structures, and linear and nonlinear optical as well as dielectric properties of three imidazolium lead bromides, IMPbBr3, IM2PbBr4, and IM3PbBr5 (IM+ = imidazolium). We show that these compounds exhibit three distinct structure types. IMPbBr3 crystallizes in the 4H-hexagonal perovskite structure with face- and corner-shared PbBr6 octahedra (space group P63/mmc at 295 K), IM2PbBr4 adopts a one-dimensional (1D) double-chain structure with edge-shared octahedra (space group P1̅ at 295 K), while IM3PbBr5 crystallizes in the 1D single-chain structure with corner-shared PbBr6 octahedra (space group P1̅ at 295 K). All compounds exhibit two structural phase transitions, and the lowest temperature phases of IMPbBr3 and IM3PbBr5 are noncentrosymmetric (space groups Pna21 at 190 K and P1 at 100 K, respectively), as confirmed by measurements of second-harmonic generation (SHG) activity. X-ray diffraction and thermal and Raman studies demonstrate that the phase transitions feature an order-disorder mechanism. The only exception is the isostructural P1̅ to P1̅ phase transition at 141 K in IM2PbBr4, which is of a displacive type. Dielectric studies reveal that IMPbBr3 is a switchable dielectric material, whereas IM3PbBr5 is an improper ferroelectric. All compounds exhibit broadband, highly shifted Stokes emissions. Features of these emissions, i.e., band gap and excitonic absorption, are discussed in relation to the different structures of each composition.