Oil spill accidents and oil-contaminated wastewater release from industries cause severe environmental pollution, resource waste, and economic loss. Thus, there is a dire need for an efficient oil/water separation approach to mitigate the challenge. Among the various oil/water separation technologies, employing oil-absorbing materials is one of the most effective strategies. In this work, a highly effective elastomer foam based on styrene–ethylene–butylene–styrene (SEBS) and ethylene propylene diene monomer (EPDM) blend was developed. Dicumyl peroxide was employed as a radical initiator for the crosslinking of the elastomer blend. The crosslinking of the blend significantly increased the melt strength of the SEBS/EPDM blend and therefore allowed them to expand extensively (up to 1200 vol %) with substantial volume increase (expansion ratio 12.8–13.1) and created pores with well-defined structures. As a result, the material exhibited outstanding oil absorption (up to 1030 wt %) due to an enlarged surface area and blend constituents. The incorporation of EPDM and radical-mediated crosslinking prevented the dissolution of SEBS in the oil and maintained the structural integrity of the foam in the oil, paving the way for recyclability. Also, the inherent hydrophobicity of employed polymers led to poor interaction with water and, thus, outstanding oil/water separation ability of the developed elastomer foams. Additionally, the foaming of triblock polymers, including SEBS, remained largely unexplored. This study has elucidated the impact of crosslinking and rheological factors on the successful foaming of SEBS.