We have performed experimental and theoretical investigation of the formation and behavior of Coulomb clusters of charged diamagnetic particles in a cusp magnetic trap under microgravity conditions aboard the International Space Station. Graphite particles of 100-400 μm in size were used in experiments due to the highest specific magnetic susceptibility. We have observed the formation of clusters in the shape of an oblate ellipsoid of revolution and their oscillations after dynamical action by changing the magnetic field. Observing the excitation and damping of oscillations we have made some estimations. Molecular dynamics simulations of the observed processes have been made. Their results are in reasonable agreement with experiments. Some differences are evidently due to some unaccounted-for reasons.