We present results for the mechanical characterization of a bisphenol-A acrylate-based polymer optical fiber (POF) manufactured using a novel light polymerization spinning (LPS) process. The particular manufacturing process allows the development of POFs having unique mechanical characteristics, which result from an exceptionally low Young's modulus. The lower Young's modulus enables optical sensors for measuring stress or pressure with improved sensitivity and potentially a higher tunable mechanical range than conventional POFs. Moreover, properties such as the storage modulus variations with respect to the temperature and humidity were studied. Fiber Bragg gratings (FBGs), were inscribed in the POF using the plane-by-plane femtosecond laser, direct-write method for selective FBG mode excitation, and were characterized for changes to temperature, pressure, and relative humidity. The response of FBGs in this LPS-POF for all the three aforementioned measurands was several times higher than that measured for conventional POFs.