Using an extended set of multi-epoch high resolution high signal-to-noise ratio optical spectra, we re-address the multiplicity properties of the O-type stars in IC 2944 and in the Cen OB2 association. We present new evidence of binarity for five objects and we confirm the multiple nature of another two. We derive the first orbital solutions for HD 100099, HD 101436 and HD 101190 and we provide additional support for HD 101205 being a quadruple system. The minimal spectroscopic binary fraction in our sample is f_min_=0.57. Using numerical simulations, we show that the detection rate of our observational campaign is close to 90%, leaving thus little room for undetected spectroscopic binary systems. The statistical properties of the O-star population in IC 2944 are similar, within the uncertainties, to the results obtained in the earlier papers in this series despite the fact that sample size effects limit the significance of the comparison. Using newly derived spectroscopic parallaxes, we reassess the distance to IC 2944 and obtained 2.3+/-0.3kpc, in agreement with previous studies. We also confirm that, as far as the O stars are concerned, the IC 2944 cluster is most likely a single entity.