Controllable trajectories of beams are one of the main themes in optical science. Here, we investigate the propagation dynamics of Laguerre-Gaussian (LG) solitons in parabolic potential wells and introduce off-axis and chirp parameters (which represent the displacement and the initial angle of beams) to make solitons sinusoidally oscillate in the x and y directions and undergo elliptically or circularly spiraling trajectories during propagation. Additionally, LG solitons with different orders and powers can be combined into soliton arrays of various shapes, depending on the off-axis parameter. Moreover, the soliton arrays can exhibit periodic converging, rotating, and other evolution behaviors, by the proper choice of the chirp parameter. A series of interesting examples demonstrate typical propagation scenarios. Our results may provide a new perspective on and stimulate further investigations of multisoliton interactions in potential wells and may find applications in optical communication and particle control.