In the context of human interactive robotics, there is a growing interest in Series Elastic Actuators (SEA), driven by the critical need to ensure safety and functionality. Moreover, a precise model is required to obtain optimal control. However, the inherent nonlinearities of those actuators, such as friction, gear backlash, and noise, greatly increase the challenge of controlling and modeling such devices. Furthermore, a compliant element adds a new nonlinearity, making the modeling task more challenging. Aiming to tackle these issues, this work proposes extensive system identification to obtain mathematical models characterizing the dynamics of an original low-cost elastomer-based SEA. The proposed methodologies investigate different characteristics of the system. The first focuses on modeling the elastic joint s nonlinearities through a hybrid model. The second contribution aims to examine the accuracy of physics-informed neural networks for gray-box identification of friction parameters. Lastly, a framework to obtain the states of the assembly using video is proposed. From these estimations, a gray-box identification using video is proposed. All three studies use the data from the actuator assembly. The first two contributions obtained important results indicating the efficiency of the proposed methodologies. The third contribution showed the potential of the novel video-based identification approach.