Substantial evidence in support of the formation of opioid receptor (OR) di-/oligomers suggests previously unknown mechanisms used by these proteins to exert their biological functions. In an attempt to guide experimental assessment of the identity of the minimal signaling unit for ORs, we conducted extensive coarse-grained (CG) molecular dynamics (MD) simulations of different combinations of the three major OR subtypes, i.e., μ-OR, δ-OR, and κ-OR, in an explicit lipid bilayer. Specifically, we ran multiple, independent MD simulations of each homomeric μ-OR/μ-OR, δ-OR/δ-OR, and κ-OR/κ-OR complex, as well as two of the most studied heteromeric complexes, i.e., δ-OR/μ-OR and δ-OR/κ-OR, to derive the preferred supramolecular organization and dimer interfaces of ORs in a cell membrane model. These simulations yielded over 250 microseconds of accumulated data, which correspond to approximately 1 millisecond of effective simulated dynamics according to established scaling factors of the CG model we employed. Analysis of these data indicates similar preferred supramolecular organization and dimer interfaces of ORs across the different receptor subtypes, but also important differences in the kinetics of receptor association at specific dimer interfaces. We also investigated the kinetic properties of interfacial lipids, and explored their possible role in modulating the rate of receptor association and in promoting the formation of filiform aggregates, thus supporting a distinctive role of the membrane in OR oligomerization and, possibly, signaling.