We derive cluster parameters and mass functions from new UBVRI CCD photometric observations of ~3500 stars reaching down to V ~20mag for the distant southern open star clusters NGC 3105, NGC 3603, Melotte 105, Hogg 15, NGC 4815, Pismis 20 and NGC 6253. For NGC 3105 and Hogg 15, CCD data are presented for the first time. The reddening is non-uniform across the face of the young (age < 300Myr) clusters NGC 3105, NGC 3603, Melotte 105, Hogg 15 and Pismis 20, with average values of E(B-V)=1.06, 1.44, 0.52, 1.15 and 1.20mag respectively, while it is uniform with average values of E(B-V)=0.72 and 0.20mag for the older clusters NGC 4815 and 6253 respectively. The values of colour excess ratios indicate the presence of normal interstellar reddening across the cluster regions studied here. Well-defined main sequences can be seen in all the clusters. However, main-sequence turn-off points and subgiant branches are well defined only in the older clusters NGC 4815 and 6253. The distances to the clusters NGC 3105, NGC 3603, Melotte 105, Hogg 15, NGC 4815, Pismis 20 and NGC 6253 are 9.5±1.5, 7.2±1.2, 2.3±0.2, 3.0±0.3, 2.75±0.2, 3.55±0.35 and 1.8±0.12kpc respectively, while the corresponding ages derived using theoretical convective core overshooting stellar evolutionary isochrones are 25±10, 3±2, 250±30, 6±2, 400±50, 6±2 and 2500±600Myr respectively. In the mass range ~1-75M⊙, the mass functions of all clusters except for NGC 6253 have been studied. The slopes of their mass spectra agree within errors with the Salpeter value (1.35). The slope of the mass function for stars more massive than 10M⊙ is almost the same as for the lower mass stars. The mass function slopes of clusters younger than 500Myr seem to have no dependence on Galactic longitude, Galactocentric distance and cluster age. As the inherent uncertainties in the mass function determinations of young Galactic star clusters can produce internal scatter that is larger than the external scatter, we conclude that, above 1M⊙, the initial mass function is universal with a slope of Salpeter value.