Morphological characteristics and mechanical properties of a series of block-double-graft (BDG) copolymers and terpolymers polystyrene-[1,2-polybutadiene-g-X-2] (X = 1,4-polybutadiene, polyisoprene, polystyrene, and polystyrene-b-polylisoprene diblocks) were investigated by transmission electron microscopy (TEM), small-angle X-ray scattering (SAXS), and tensile testing. All BDG materials have linear polystyrene-1,2-polybutadien (PS-b-1,2-PBD) diblock copolymer backbones. Two identical branches are grafted at every randomly distributed tetrafunctional junction point on the 1,2-PBD part of the backbone. Standard microstructures, such as body-center-cubic spheres, hexagonally packed cylinders, and lamellae, are obtained at different total PS volume fractions. It is found that when the branches are polydienes, the BDG molecules form the same morphologies as their linear diblock counterparts. In such cases, phase separation occurs between the polystyrene domain and a combined diene microdomain formed by the backbone 1,2-PBD part and the polydiene branches. In BDG materials in which the branches are polystyrene-polyisoprene diblock copolymers, lamellae are obtained at a total PS volume fraction close to 0.50. It is found that the domain spacings of these materials are predominately determined by the molecular weights of the diblock branches instead of the backbones. A lamellae-forming BDG terpolymer,with an average of three tetrafunctional junction points per molecule exhibited characteristic thermoplastic elastomer properties with a stress at break of 32 MPa and strain at break of 1000%. It is proposed that the high strength of this BDG terpolymer is attributed to the chain conformation in the microphase-separated state. The elastic PBD blocks of the backbone bridge adjacent PS domains through multiple junction points, resulting in the enhanced elastomeric properties. Several parameters are found to influence the mechanical properties of these BDG materials: (1) the existence of backbone PS, (2) the molecular weight of the branches, and (3) the number and functionality of branch points on the 1,2-PBD part of the backbone.