We report intrinsic tunneling data for mesa structures fabricated on three over- and optimally-doped Bi2.15Sr1.85CaCu2O8+δ crystals with transition temperatures of 86-78 K and 0.16-0.19 holes per CuO2 unit, for a wide range of temperature (T) and applied magnetic field (H), primarily focusing on one overdoped crystal (OD80). The differential conductance above the gap edge shows a clear dip structure which is highly suggestive of strong coupling to a narrow boson mode. Data below the gap edge suggest that tunnelling is weaker near the nodes of the d-wave gap and give clear evidence for strong T-dependent pair breaking. These findings could help theorists make a detailed Eliashberg analysis and thereby contribute towards understanding the pairing mechanism. We show that for our OD80 crystal the gap above Tc, although large, is reasonably consistent with the theory of superconducting fluctuations.