We report specialized interplane magnetoresistance (MR) measure-ments on the organic superconducting compound β''-(BEDT-TTF)2SF5CH2CF2SO3 (where BEDT-TTF is bis(ethylenedithio)tetrathiafulvalene) in both the superconducting (Tc ~ 5 K) and normal states versus magnetic field direction. In the normal state, detailed angular-dependent magnetoresistance oscillation (AMRO) studies reveal peculiar features of the Fermi surface topology of this compound, and very high magnetic field studies further support the unusual nature of the electronic structure. In the superconducting state we investigate, through detailed AMRO measurements, the anomalous MR peak that appears within the superconducting field-temperature phase diagram. Our results reveal a direct connection between the superconducting state determined from purely in-plane field, and the vortex lattice produced by the inter-plane magnetic field. We also describe several unique sample rotation instruments used in these high field experiments, including the use of dysprosium pole pieces in combination with a 45 T hybrid magnet to carry out measurements at the highest steady-state resistive magnetic field (47.8 T) yet achieved.