The elastic and inelastic scattering of pi(+/-) and K+ mesons from the Li-6,Li-7 and Be-9 nuclei are analyzed in the Glauber-Sitenko diffraction theory. It is shown that the Glauber-Sitenko theory combined with wave functions obtained in the potential cluster models can describe many properties of the elastic and inelastic scattering of various particles in a wide energy range. The interaction features of various particles-protons, pi(+/-) and K+ mesons-incident on nucleons are compared by analyzing hadron-nucleon amplitudes at the quark level. The relation of elementary interaction to the parameters of phenomenological amplitudes and to the behavior of observables is determined. The differential cross sections are related to the cluster potentials, which are used to calculate the wave functions of target nuclei. The types of potentials that most adequately describe the entire set of experimental data have been determined. Contributions from different multiplicities of scattering and rescattering in the Omega operator to scattering cross sections are estimated for various angular ranges. It is shown that, to reproduce the cross sections for pi(+/-) mesons in a wide range of angles and momentum transfers, it is necessary to take into account all the multiplicities of scattering and rescattering, whereas single and double scattering are sufficient for K+ mesons. The contribution from different components of wave functions, the behavior of cross sections for various types of leading particles, and the energy dependence of cross sections are discussed. It is demonstrated by comparing our results to those calculated within the optical model and DWIA that the diffraction theory reproduces experimental data no worse and sometimes even better than these extensively used models, because more realistic wave functions are used.