Exploration of spin currents in organic semiconductors (OSECs) induced by resonant microwave absorption in ferromagnetic substrates is appealing for potential spintronics applications. Owing to the inherently weak spin-orbit coupling (SOC) of OSECs, their inverse spin Hall effect (ISHE) response is very subtle; limited by the microwave power applicable under continuous-wave (cw) excitation. Here we introduce a novel approach for generating significant ISHE signals in OSECs using pulsed ferromagnetic resonance, where the ISHE is two to three orders of magnitude larger compared to cw excitation. This strong ISHE enables us to investigate a variety of OSECs ranging from π-conjugated polymers with strong SOC that contain intrachain platinum atoms, to weak SOC polymers, to C60 films, where the SOC is predominantly caused by the curvature of the molecule's surface. The pulsed-ISHE technique offers a robust route for efficient injection and detection schemes of spin currents at room temperature, and paves the way for spin orbitronics in plastic materials.