Recent studies of molecular orientation in sheared liquid crystalline polymers have often yielded contradictory results. To check the self-consistency of methods for quantitative measurements of molecular orientation, liquid crystalline solutions of (hydroxypropyl)cellulose [HPC] and poly(benzyl glutamate) [PEG] have been studied using flow birefringence, X-ray scattering, and neutron scattering. HPC X-ray scattering patterns show an arclike pattern with a distinct peak as a function of scattering vector, while PEG patterns show a more diffuse equitorial streak. These differences are attributed to more strongly correlated lateral packing in HPC solutions due to their higher concentration. Measurements of orientation in steady shear flow agree well among the three techniques. Lyotropic HPC and PEG solutions differ in orientation at low shear rates. KPC solutions exhibit near zero orientation at low rates, while X-ray and neutron scattering measurements confirm previous birefringence data showing a low shear rate plateau of moderate orientation in PEG. Differences with recent neutron scattering measurements on PEG solutions that show low orientation at low shear rate are attributed to choice of solvent, rather than choice of technique. X-ray and optical data are consistent in showing decreasing orientation in HPC solutions during relaxation, but discrepancies are found in relaxation of PEG solutions. Large increases in flow birefringence suggest substantial orientation enhancement. X-ray data on one PEG solution confirm increasing orientation, but X-ray and neutron scattering data on a more concentrated solution show only modest changes in orientation. It is suggested that flow birefringence fails in this case due to texture coarsening to the point where there is no longer effective averaging over the distribution of director orientations along the light path.