The influence of acoustic phonons on the emission spectra of quantum dashes (QDashes), that are quasi-zerodimensional epitaxial nanostructures with significant shape anisotropy, is investigated both experimentally and theoretically. Photoluminescence (PL) spectra of single InAs/InGaAlAs/InP (001) QDashes exhibit sidebands of the main emission peak, clearly indicating the contribution of phonon-assisted emission to the exciton luminescence, which dominates the PL line shape at higher temperatures (between 50 and 100 K, usually). By utilizing the independent boson model we perform systematic and comprehensive studies of the influence of the overall geometry of quantum confinement on this spectral feature in an uncommon quantum system. A comparison of the experimental data and the results of modeling have confirmed the existence of two types of states differing in the spatial confinement and symmetry within one sample, i.e., typical for large elongated objects or characteristic for smaller and more symmetric structures. The latter are supposed to correspond to local widenings or zigzag bends present in some of the dashes and acting as additional localization centers, which confine excitons in a much smaller volume and decrease effectively the resulting in-plane anisotropy. Those observations evidence a nontrivial spatial character of the quantum confinement in these structures. They are consistent with our previous polarization-resolved study on the QDash ensemble and correlate well with the exciton decay times, and the spectral-diffusion-dominated line broadenings at low temperatures reflecting the effect of electric field fluctuations on the excitons of a different spatial extension. Finally, we demonstrate a pronounced suppression of phonon-induced decoherence for such strongly elongated nanostructures.