Kagome metals AV3Sb5 (A =K, Rb, Cs) exhibit an exotic charge order (CO), involving three order parameters, with broken translation and time-reversal symmetries compatible with the presence of orbital currents. Despite the tremendous experimental and theoretical efforts that have been invested into the characterization of this phase, its properties are still intensely debated, and it is unclear if the origin of the CO is mainly due to electron-electron or electron-phonon interactions. One of the few indications that are confirmed by the majority of experimental studies is the nematicity of this state, a feature that might be enhanced by electronic correlations irrespective of the nature of the primary instability. However, it is still unclear whether the nematic CO becomes stable at a temperature equal to (Tnem = TC) or lower than (Tnem < TC) the one of the CO itself. Here, we systematically characterize several CO configurations, some proposed for the new member of the family ScV6Sn6, by combining phenomenological Ginzburg-Landau theories, valid irrespective of the specific ordering mechanism, with mean-field analysis. We find a few configurations for the CO that are in agreement with most of the experimental findings to date and that are described by different Ginzburg-Landau potentials. Moreover, we propose to use resonant ultrasound spectroscopy to experimentally characterize the properties of the order parameters of the CO, such as the number of their components and their relative amplitude, and provide an analysis of the corresponding elastic tensors. This might help understand which mean-field configuration found in our study is the most representative for describing the CO state of kagome metals, and it can provide information regarding the nematicity onset temperature Tnem with respect to TC.