A theoretical investigation has been made on positron-acoustic (PA) Gardner solitons (GSs) and double layers (DLs) in four-component plasma system consisting of immobile positive ions, mobile cold positrons, nonthermal hot positrons, and nonthermal hot electrons. The reductive perturbation method has been used to derive Korteweg-de Vries (K-dV), modified K-dV (mK-dV), and Gardner equations. The basic features (viz. amplitude, polarity, speed, etc.) of the PA GSs as well as PA DLs are examined. The analytical comparison among K-dV solitons, mK-dV solitons, and GSs are also made. It has been identified that the amplitude, polarity, speed, thickness of such PA solitons and DLs are significantly modified due to the presence of nonthermal distributed hot electrons and hot positrons. The results of our investigation should be useful for understanding various interstellar space plasma environments (viz. ionosphere, lower part of magnetosphere, auroral acceleration regions, supernovas, pulsar environments, cluster explosions, active galactic nuclei, etc.).