We report studies of the orientation state of multiwalled carbon nanotubes (MWNTs) dispersions in steady and transient shear flows. Uncured epoxy was used as a viscous Newtonian suspending medium and samples were prepared from "aligned" MWNTs using methods previously reported [S. S. Rahatekar et al., J. Rheol. 50, 599 (2006)]. Orientation measurements were performed in both the flow-gradient (1-2) and flow-vorticity (1-3) plane of simple shear flow using in situ x-ray scattering techniques. Steady state measurements in the 1-2 plane indicate that the MWNT orientation is shear rate dependent, with the MWNTs orienting closer to the flow direction at higher shear rates. During steady shear, anisotropy was measured to be higher in the 1-2 plane than in the 1-3 plane, demonstrating that the nanotube orientation state is not unaxially symmetric in shear. It is hypothesized that the steady state MWNT orientation is governed primarily by a rate-dependent state of nanotube aggregation/disaggregation, which was separately characterized by optical microscopy of the same samples under shear. High flux synchrotron radiation allowed for time-resolved structural studies in transient flows. A partial relaxation of flow-induced anisotropy was observed following flow cessation, despite the very small rotational diffusivity estimated for these nanotubes. Long transients are observed in step-down experiments, as the orientation state changes in response to the slow tube aggregation process.