The dynamical ages and some other physical parameters of the opposite lobes of 20 subjectively selected giant radio galaxies (GRGs), as well as of their environment, are estimated using the dynage algorithm of Machalski et al. These data, supplemented with the relevant data determined for another 10 GRGs in Paper III, are used to analyse the aspects of the apparent length and luminosity asymmetries in the lobes in view of their dynamical evolution. As in Paper III, the fits give slightly different dynamical ages and other model parameters for the opposite lobes modelled independently of each other. Therefore, demanding similar values of the jet power and the radio core density for the same source, a self-consistent age solution for the opposite lobes is considered, which results in different density profiles along the lobes and different initial energy distributions of the emitting particles at their heads. The analysis shows the following. (i) The age of the longer lobe, fitted independently, tends to be younger than that for the shorter lobe. This contradicts with the axial expansion expected in a symmetrical environment (a halo) surrounding the source and strongly supports the self-consistent solution with different ambient density profiles along the opposite lobes. In the frame of the latter solution, the difference between the ages of the opposite lobes almost always diminishes, compared to that found with the independent fits, not exceeding a factor of ∼1.25. (ii) There is a clear correlation between the age ratio and the difference in radio spectra: longer lobes with a steeper spectrum in most cases are older; however, longer lobes having a flatter spectrum are mostly younger. The age difference is always larger than that expected from the unknown inclination of the jets' axis to the observer's line of sight and a pure kinematic effect. (iii) The slope of the injected (initial) radio spectrum, αinj, has a narrow distribution around a value of 0.5. Its value tends to be lower in the longer lobe than in the shorter lobe. The difference between the values of αinj in the opposite lobes is very low; a standard deviation of ∼0.02 from the mean is found. This difference increases about three times in the self-consistent solution, but always within the relatively narrow range of 0.46–0.62. (iv) There is a strong correlation between the difference in values of β (the exponent describing the external density profile) for the opposite lobes and the ratio of their volume. This is much stronger than a dependence of Δβ on the ratio of the lobes' length. This likely suggests that the environment of the GRGs is non-uniform or clumpy.