Results. We present empirical effective temperature versus spectral subtype calibrations at LMC-metallicity for giants and supergiants. The calibration for giants shows a + 1kK off set compared to similar Galactic calibrations; a shift of the same magnitude has been reported for dwarfs. The supergiant calibrations, though only based on a handful of stars, do not seem to indicate such an off set. The presence of a strong upturn at spectral type O3 and earlier can also not be confirmed by our data. In the spectroscopic and classical Hertzsprung-Russell diagrams, our sample O stars are found to occupy the region predicted to be the core hydrogen-burning phase by state-of-the-art models. For stars initially more massive than approximately 60 M-circle dot, the giant phase already appears relatively early on in the evolution; the supergiant phase develops later. Bright giants, however, are not systematically positioned between giants and supergiants at M-init >= 25 M-circle dot At masses below 60 M-circle dot, the dwarf phase clearly precedes the giant and supergiant phases; however this behavior seems to break down at Minit <= 18 M-circle dot Here, stars classified as late O III and II stars occupy the region where O9.5-9.7 V stars are expected, but where few such late OV stars are actually seen. Though we can not exclude that these stars represent a physically distinct group, this behavior may reflect an intricacy in the luminosity classification at late O spectral subtype. Indeed, on the basis of a secondary classification criterion, the relative strength of Si IV to He I absorption lines, these stars would have been assigned a luminosity class IV or V. Except for five stars, the helium abundance of our sample stars is in agreement with the initial LMC composition. This outcome is independent of their projected spin rates. The aforementioned five stars present moderate projected rotational velocities (i.e., 3 v(e) sin i < 200 km s(-1)) and hence do not agree with current predictions of rotational mixing in main-sequence stars. They may potentially reveal other physics not included in the models such as binary-interaction effects. Adopting theoretical results for the wind velocity law, we find modified wind momenta for LMC stars that are similar to 0.3 dex higher than earlier results. For stars brighter than 10(5) L-circle dot, that is, in the regime of strong stellar winds, the measured (unclumped) mass-loss rates could be considered to be in agreement with line-driven wind predictions if the clump volume filling factors were f(V) similar to 1/ 8 to 1/6.