Impulsive laser excitation of molecules can create rotational wave packets that lead to transient alignment or orientation. We present a theoretical analysis of the signatures of post-pulse field-free time-dependent alignment and orientation of diatomic molecules in time-resolved nonresonant x-ray scattering. This shows that alignment and its time dependence due to the interference terms of the rotational wave packet are visible in the x-ray scattering signal whereas signatures of orientation and its time dependence are absent. To that end, we discuss the time dependence of the coherent rotational motion associated with electronically resonant one-photon excitations. We illustrate our findings with calculated two-dimensional scattering signals for the sodium fluoride molecule (NaF) in the gas phase.