Soft robots hold great promise but are notoriously difficult to control due to their compliance and back-drivability. In order to implement useful controllers, improved methods of perceiving robot pose (position and orientation of the entire robot body) in free and perturbed states are needed. In this work, we present a holistic approach to robot pose perception in free bending and with external contact, using multiple soft strain sensors on the robot (not collocated with the point of contact). By comparing the deviation of these sensors from their value in an unperturbed pose, we are able to perceive the mode and magnitude of deformation and thereby estimate the resulting perturbed pose of the soft actuator. We develop a sample 2 degree-of-freedom soft finger with two sensors, and we characterize sensor response to front, lateral, and twist deformation to perceive the mode and magnitude of external perturbation. We develop a data-driven model of free-bending deformation, we impose our perturbation perception method, and we demonstrate the ability to perceive perturbed pose on a single-finger and a two-finger gripper. Our holistic contact identification method provides a generalizable approach to perturbed pose perception needed for the control of soft robots.