Poly(styrene-b-ethylene-co-butylene-b-styrene) (SEBS)/organophilic halloysite nanotube (Org-HNT) nanocomposites were prepared by solution mixing and then compression molded. Maleic anhydride grafted SEBS (SEBS-g-MA) was also used as a compatibilizer in preparation of SEBS/SEBS-g-MA/Org-HNT ternary nanocomposites. Surface morphologies and both static and dynamic mechanical analyses as well as thermal stabilities of the nanocomposites were carried out. Both the binary and ternary nanocomposites exhibited higher tensile moduli, tensile strength, and toughness values compared to neat SEBS. The elastic modulus was found to increase about 385% and 320% with addition of 3 and 5 phr Org-HNT into the SEBS matrix, respectively, while the maximum toughness was achieved via SEBS-5H composite with an increase of 45%. The ternary nanocomposite having 3 phr Org-HNT and 10 phr SEBS-g-MA (3H10SMA) gave about a 325% and 103% increase in the elastic modulus and toughness, respectively, together with a 75% increase in the tensile strength as the maximum value. This result was ascribed to interactions of the surface of the nanotubes with the maleic anhydride (MA) group of the compatibilizer. The same nanocomposite was also found to have two times higher dynamic storage modulus at 25°C than neat SEBS and almost the same damping value, which is an indication of improvement in the elastic character of SEBS without impairing its damping ability. Although a much higher damping value was obtained via use of 20 phr SEBS-g-MA with the same amount of nanotubes, the corresponding storage modulus decreased too much, close to that of neat SEBS. The enhanced tensile modulus, strength, and toughness of the 3H10SMA nanocomposite, which is consistent with its dynamic mechanical properties, indicate a good balance between the toughness/damping and stiffness. Moreover, all the nanocomposites exhibited better thermal stabilities than neat SEBS, showing higher midpoint degradation temperatures and peak maximum temperatures at which the maximum degradation occurs.