Multiplicity is one of the most fundamental observable properties of massive O-type stars and offers a promising way to discriminate between massive star formation theories. Nevertheless, companions at separations between 1 and 100 milli-arcsec (mas) remain mostly unknown due to intrinsic observational limitations. At a typical distance of 2 kpc, this corresponds to projected physical separations of 2-200 AU. The Southern MAssive Stars at High angular resolution survey (smash+) was designed to fill this gap by providing the first systematic interferometric survey of Galactic massive stars. We observed 117 O-type stars with VLTI/PIONIER and 162 O-type stars with NACO/SAM, respectively probing the separation ranges 1-45 and 30-250 mas and brightness contrasts of ∆H < 4 and ∆H < 5. Taking advantage of NACO's field-of-view, we further uniformly searched for visual companions in an 8 -radius down to ∆H = 8. This paper describes the observations and data analysis, reports the discovery of almost 200 new companions in the separation range from 1 mas to 8 and presents the catalog of detections, including the first resolved measurements of over a dozen known long-period spectroscopic binaries.Excluding known runaway stars for which no companions are detected, 96 objects in our main sample (δ < 0 • ; H < 7.5) were observed both with PIONIER and NACO/SAM. The fraction of these stars with at least one resolved companion within 200 mas is 0.53. Accounting for known but unresolved spectroscopic or eclipsing companions, the multiplicity fraction at separation ρ < 8 increases to f m = 0.91 ± 0.03. The fraction of luminosity class V stars that have a bound companion reaches 100% at 30 mas while their average number of physically connected companions within 8 is f c = 2.2 ± 0.3. This demonstrates that massive stars form nearly exclusively in multiple systems. The nine non-thermal radio emitters observed by smash+ are all resolved, including the newly discovered pairs HD 168112 and CPD−47 • 2963. This lends strong support to the universality of the wind-wind collision scenario to explain the non-thermal emission from O-type stars.