Rheological properties of polymer melts under weak flow reflect the orientational anisotropy of the chains, which is established experimentally as the validity of the stress-optical rule (SOR). In contrast, SOR fails under strong flow, and no rigid expression of the properties in terms of the chain conformation has been established. In this study, we have carried out a systematic analysis using atomistic nonequilibrium molecular dynamics (NEMD) simulations on the scaling behavior of chain rotational dynamics and rheological properties for unentangled and entangled linear polymer melts under shear in a wide range of flow strengths in connection with the underlying molecular characteristics. Directly comparing the rheological properties and chain conformations obtained from the NEMD simulations for linear polymers under strong shear flow, we present scaling of the properties with respect to structural parameters in a sense similar to an experimental attempt of correlating theological and structural data. For the critical angle theta(c) (that balances the advective and diffusive chain rotational dynamics), the maximum chain-stretch angle theta(Max stretch), and the associated rotational diffusion (D-theta c) and translational hydrodynamic friction (zeta(parallel to)) coefficients, we first analyze their scaling behavior with respect to the Weissenberg number (Wi). The analysis shows that the chain residence time in the critical angular regime primarily determines the overall scaling behavior of the characteristic rotational time tau(rot). Furthermore, comparing the Wi dependence of the structural parameters (defined for the whole chain backbone and/or entanglement strand) and rheological properties, we examine the scaling of those properties with respect to the structural parameters. Specifically, in the intermediate flow regime, we find scaling relationships for the viscosity eta and the first normal stress difference psi(i) with respect to the well-known fundamental molecular characteristics in polymer rheology such as the chain orientation, chain stretch, and interchain entanglement: (i) eta similar to theta R-alpha 1(2) and psi i similar to theta R-alpha 2(2) with alpha(l) = (1.5-1.7) and alpha(2) = (3.2-3.6) for unentangled melts and (ii) eta similar to theta(alpha 1)(es)Z(gamma 1)d(es)(2) and psi 1 similar to theta(alpha)(es)2Z(gamma 2)d(es)(2) with gamma(1) = (3.8-4.0) and gamma(2) = (2.1 2.4) for entangled melts. Here, theta(theta(es)), R, Z, and d(es) are the average chain orientation angle (that of entanglement strand), the mean chain end-to-end distance, the average number of interchain entanglements, and the average length of an entanglement strand, respectively. Under moderately strong flow, these relationships may serve as a supplement (or substitute) for SOR, which has a rigid molecular basis under slow flow. In the strong flow regime, the above scaling expressions become invalid and another empirical rheological scaling is found in terms of the characteristic rotational time tau(rot )as the representative dynamic variable to accommodate intermolecular collisional effects: (iii) eta similar to tau(delta 2)(rot) and psi(1) similar to tau(delta 2)(rot) with delta(1) = (0.5-0.6) and delta(2) = (1. 8-2.0) for both unentangled and entangled systems.