In underwater environment, wireless signal propagation is very challenging, and strongly affected by absorption- and scattering-induced attenuation losses. Optical wireless communications (OWC), due to huge bandwidths, can provide high data rates and medium propagation ranges, representing a viable technology for underwater scenarios. There are several statistical distributions that model the effect of underwater turbulence on OWC, and how to model the underwater OWC (UOWC) channel with higher accuracy is still a topic to investigate. In this paper, we investigate the use of intelligent reflecting surfaces (IRSs) for enhancing performance in underwater OWC systems. In this regard, we present a unified channel model for UOWC, working both for heterodyne and intensity modulated/direct detection (IM/DD) schemes. The analytical expressions of average bit-error-rate (BER), outage probability, and channel capacity are derived including the combined effect of (i) attenuation, (ii) turbulence, (iii) pointing error, and (iv) angle-of-arrival (AOA) fluctuations to ensure the comprehensive characterization of underwater optical wireless communication channel. To make the analysis and results more realistic, the practical scenarios and parameters are considered. The probability density function (PDF) and the cumulative distribution function (CDF) of the underwater OWC channel are obtained analytically. Simulation results are presented for various parameters of underwater channel and communication systems. It is observed that the application of IRS remains as an important tool in terms of mitigating the overall fading effect caused by the combination of previous phenomena in underwater wireless channel. Also, the benefits of heterodyne detection over IM/DD is evinced.