Solid parahydrogen (p-H2) is known to support long-lived coherences, of the order of 100 ps, which enables high-resolution spectroscopy in the time domain. Rotational Raman-type excitations to sublevels of J = 2 are delocalized due to electric-quadrupole-quadrupole coupling in p-H2 crystals, and the resulting states can be characterized as rotons. Wave packets of rotons exhibit molecular alignment with respect to laboratory coordinates. Here the concept of field-free molecular alignment, induced by strong ultrashort laser pulses, is extended into a molecular solid case. We derive a solid-state analog for the gas-phase alignment measure and illustrate the time-dependent alignment degree in p-H2 crystals by numerical simulations. To underscore the Raman gain effect of the solid, general properties of the field-free alignment are revisited by comparing gaseous p-H2 with N2. The interplay between the polarization direction of the excitation pulses and the axis directionality of the crystal is shown to affect the alignment dynamics via the spatial (M =0, ±1, ±2) composition of the roton wave packets. We simulate experimental traces by incorporating the induced alignment degree in the calculation of heterodyne-detected realization of femtosecond pump-probe optical Kerr effect spectroscopy. With the help of dispersed, two-dimensional resolved images of the calculated signal we reproduce the experiment as a whole. To that end, the effects of probe chirp, shape, and power must be explored in detail. We find good agreement with previous experiments and unravel the ambiguity of tracing back the wave-packet composition from the signal; in particular, we find that the effect of quantum phase factors of all the components should be taken into account when explaining the signal properties. [ABSTRACT FROM AUTHOR]