  We develop a microscopic theory of finite-temperature spin-nematic orderings
in three-dimensional spatially anisotropic magnets consisting of weakly-coupled
frustrated spin-1/2 chains with nearest-neighbor and next-nearest-neighbor
couplings in a magnetic field. Combining a field theoretical technique with
density-matrix renormalization group results, we complete finite-temperature
phase diagrams in a wide magnetic-field range that possess spin-bond-nematic
and incommensurate spin-density-wave ordered phases. The effects of a four-spin
interaction are also studied. The relevance of our results to
quasi-one-dimensional edge-shared cuprate magnets such as LiCuVO4 is discussed.
