Polyethylene-based ternary nanocomposites were prepared with different clay structures, obtained by the modification of purified Resadiye bentonite as the reinforcement, a random terpolymer of ethylene, butyl acrylate, and maleic anhydride with the trade name Lotader3210 as the compatibilizer, and linear low-density polyethylene (LLDPE) as the polymer matrix in an intensive batch mixer. The quaternary ammonium/phosphonium salts used for the modification of bentonite were dimethyldioctadecyl ammonium (DMDA) chloride (Cl), tetrakisdecyl ammonium (TKA) bromide (Br), and tributylhexadecyl phosphonium (TBHP) Br. The effects of the physical properties and structure of the organoclay on the clay dispersion were studied at different clay contents (2 and 5 wt %) and at a compatibilizer/organoclay ratio of 2.5. The extent of organoclay dispersion was determined by X-ray diffraction (XRD) and was verified by transmission electron microscopy (TEM), mechanical testing, and rheological analysis. XRD analysis showed that the nanocomposite with the organoclay DMDA contained intercalated silicate layers, as also verified by TEM. The TEM analysis of the nanocomposites with TBHP exhibited intercalated/partially exfoliated clay dispersion. TKA, with a crowded alkyl environment, sheltered and hindered the intercalation of polymer chains through the silicate layers. In comparison to pure LLDPE, nanocomposites with a 33-41% higher Young's modulus, 16-9% higher tensile strength, and 75-144% higher elongation at break were produced with DMDA and TBHP, respectively (at 5 wt % organoclay). The storage modulus increased by 807-1393%, and the dynamic viscosity increased by 196-339% with respect to pure LLDPE at low frequencies for the samples with DMDA and TBHP (at 5 wt % organoclay).