Autonomous underwater vehicles (AUVs) play an increasing important role in deep-sea exploration these years. This work first presents comprehensive analyses on AUV-based underwater wireless optical communication (UWOC) uplinks, where non-orthogonal multiple access (NOMA) is adopted to facilitate the spectral efficiency. The laser beam irradiance fluctuation is assumed to follow the Weibull–generalized gamma (WGG) distribution. Besides, the beam spread function (BSF) is adopted to depict the attenuation triggered by absorption, scattering, and misalignment. To begin with, the exact closed-form expressions of the probability density function (PDF), cumulative distribution function (CDF), and moments are presented. Furthermore, both perfect successive interference cancellation (pSIC) and imperfect SIC (ipSIC) scenarios are analyzed, respectively. With either fixed decoding order SIC (f-SIC) or dynamic decoding order SIC (d-SIC) scheme at the receiver, both exact and asymptotic results of the outage probability and ergodic sum-rate are derived. The diversity orders are also derived through the asymptotic outage probability. Besides, the average bit error performance is illustrated by conditional bit error rate (BER). Results show that the outage threshold significantly impact the outage performance. Moreover, the residual interference induced by non-ideal SIC would result in a constant value of the Fox's H function and further lead to outage error floors and capacity bounds, which indicates that the performance of this UWOC system depends largely on the advanced SIC receiver. The impacts of turbulence strength, detecting methods, decoding strategies, and power levels difference are also analyzed in detail. All the derivations are verified via Monte-Carlo simulations.