In this work, we study 2.1 nm-diameter uniaxial strained Si gate-all-around nanowire field-effect transistors, focusing on the electron mobility and the variability due to random discrete dopants (RDDs). Firstly, we extract the electron effective masses under various strains from Density Functional Theory (DFT) simulations. Secondly, we explore the impact of strain on the electron mobility in the Si nanowire using the Kubo-Greenwood formalism with a set of multi-subband phonon, surface roughness, and ionized impurity scattering mechanisms. Finally, we perform quantum transport simulations to investigate the effect of RDDs on the threshold voltage and the ON-state current variation.