Context: .This is the third of a series of papers on simulating the mechanisms acting currently on the Oort cloud and producing the observed long-period comets.Aims.In this paper we investigate the influence of current stellar perturbers on the Oort cloud of comets under the simultaneous galactic disk tide. We also analyse the past motion of the observed long-period comets under the same dynamical model to verify the widely used definition of dynamically new comets. Methods.The action of nearby stars and the galactic disk tide on the Oort cloud was simulated. The original orbital elements of all 386 long-period comets of quality classes 1 and 2 were calculated, and their motion was followed numerically for one orbital revolution into the past, down to the previous perihelion. We also simulated the output of the close future pass of GJ 710 through the Oort cloud. Results.The simulated flux of the observable comets resulting from the current stellar and galactic perturbations, as well as the distribution of perihelion direction, was obtained. The same data are presented for the future passage of GJ 710. A detailed description is given of the past evolution of aphelion and perihelion distances of the observed long-period comets. Conclusions. We obtained no fingerprints of the stellar perturbations in the simulated flux and its directional structure. The mechanisms producing observable comets are highly dominated by galactic disk tide because all current stellar perturbers are too weak. Also the effect of the close passage of the star GJ 710 is very difficult to recognise on the background of the Galactic-driven observable comets. For the observed comets we found only 45 to be really dynamically "new" according to our definition based on the previous perihelion distance value.