Continuum manipulators (CMs) are widely used in minimally invasive procedures due to their compliant structure and ability to navigate deep and confined anatomical environments. However, their distributed deformation makes force sensing, contact detection, localization, and force estimation challenging, particularly when interactions occur at unknown arc-length locations along the robot. To address this problem, we propose a cascade learning-based framework (CLF) for CMs instrumented with a single distributed Optical Frequency Domain Reflectometry (OFDR) fiber embedded along one side of the robot. The OFDR sensor provides dense strain measurements along the manipulator backbone, capturing strain perturbations caused by external interactions. The proposed CLF first detects contact using a Gradient Boosting classifier and then estimates contact location and interaction force magnitude using a CNN--FiLM model that predicts a spatial force distribution along the manipulator. Experimental validation on a sensorized tendon-driven CM in an obstructed environment demonstrates that a single distributed OFDR fiber provides sufficient information to jointly infer contact occurrence, location, and force in continuum manipulators.