We investigate the enhancement of star formation efficiency in galaxy interactions and mergers by numerical simulations of several hundred galaxy collisions. All morphological types along the Hubble sequence are considered in the initial conditions of the two colliding galaxies, with varying bulge-to-disk ratios and gas mass fractions. Different types of orbits are simulated, direct and retrograde, according to the initial relative energy and impact parameter, and the resulting star formation history is compared to that occuring in the two galaxies when they are isolated. Our principal results are (1) retrograde encounters have greater star formation efficiency (SFE) than direct encounters, (2) the amount of gas available in the galaxy is not the main parameter governing the SFE in the burst phase, (3) there is a negative correlation between the amplitude of the star forming burst and the tidal forces exerted per unit of time, which is due to the large amount of gas dragged outside the galaxy by tidal tails in strong interactions, (4) globally, the Kennicutt-Schmidt law is seen to apply statistically for isolated galaxies, interacting pairs and mergers, (5) enhanced star formation occurs essentially in nuclear starbursts, triggered by inward gas flows driven by non-axisymmetries in the galaxy disks. Direct encounters develop more pronounced asymmetries than retrograde ones. Based on these statistical results we derive general laws for the enhancement of star formation in galaxy interactions and mergers, as a function of the main parameters of the encounter.