Context. This paper contains results from the first 30 months of the NELIOTA project for near-Earth objects and meteoroids impacting the lunar surface. We present our analysis of the statistics concerning the efficiency of the campaign and the parameters of the projectiles and those of their impacts. Aims. The parameters of the lunar impact flashes are based on simultaneous observations in two wavelength bands. They are used to estimate the distributions of the masses, sizes, and frequency of the impactors. These statistics can have applications in both space engineering and science. Methods. The photometric fluxes of the flashes are measured using aperture photometry and their apparent magnitudes are calculated using standard stars. Assuming that the flashes follow a black body law of irradiation, the temperatures can be derived analytically, while the parameters of the projectiles are estimated using fair assumptions on their velocity and luminous efficiency of the impacts. Results. There have been 79 lunar impact flashes observed with the 1.2 m Kryoneri telescope in Greece. The masses of the meteoroids range between 0.7 g and 8 kg, and their respective sizes between 1 and 20 cm, depending on their assumed density, impact velocity, and luminous efficiency. We find a strong correlation between the observed magnitudes of the flashes and the masses of the meteoroids. Moreover, an empirical relation between the emitted energies of each band has been derived, allowing for an estimation of the physical parameters of the meteoroids that produce low energy impact flashes. Conclusions. The NELIOTA project has so far the highest detection rate and the faintest limiting magnitude for lunar impacts compared to other ongoing programs. Based on the impact frequency distribution on the Moon, we estimate that sporadic meteoroids with typical masses less than 100 g and sizes less than 5 cm enter the mesosphere of the Earth with a rate of ~108 meteoroids h⁻¹ and also impact Moon with a rate of ~8 meteoroids h⁻¹.