The order-disorder transition (ODT) and the ordering kinetics have been studied in four-arm star diblock copolymer melts of styrene (corona) and isoprene (core) by rheology and SAXS. The results are compared with the corresponding linear diblock and show that the transition shifts in the direction predicted by theory. The mean-field structure factor is used to describe the SAXS profiles at T much greater than T-ODT and to extract the temperature dependence of the interaction parameter (chi)(T). Because of the weak T dependence of (chi), we can explore only a small region of the phase diagram, namely, 16.5 < N-chi(0) < 14.6, for f(PS) = 0.25. The microphase-separated state consists of spherical microdomains of the minor component(PS) which resembles a bcc phase, however, not with the full symmetry. To explore the morphology over a broader T range, we use the results of computer simulation on equivalent chains, which for f(PS) = 0.25 provide the following succession of phases : hexagonal - a bicontinuous structure which resembles the gyroid - body-centered cubic (bcc) - disordered. The existence of a stable gyroid phase-over a limited composition range-is also predicted by a theory based on a calculation of the higher harmonics. Fluctuation corrected phase diagrams for four-arm star block copolymers are presented here, for the first time. The ordering kinetics have been studied by rheology and show a dramatic slowing of the ordering process as compared to symmetric and asymmetric linear diblocks as a result of the molecular topology and constrained mobility of chains.