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 milliarcsec (mas) remain mostly unknown due to intrinsic observational limitations. At a typical distance of 2kpc, this corresponds to projected physical separations of 2-200AU. 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/Sparse Aperture Masking (SAM), probing the separation ranges 1-45 and 30-250mas and brightness contrasts of {Delta}H<4 and {Delta}H<5, respectively. Taking advantage of NACO's field of view, we further uniformly searched for visual companions in an 8" radius down to {Delta}H=8. This paper describes observations and data analysis, reports the discovery of almost 200 new companions in the separation range from 1mas to 8" and presents a 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 ({delta}<0{deg}; H<7.5) were observed both with PIONIER and NACO/SAM. The fraction of these stars with at least one resolved companion within 200mas is 0.53. Accounting for known but unresolved spectroscopic or eclipsing companions, the multiplicity fraction at separation {rho}<8" increases to f_m_=0.91+/-0.03. The nine non-thermal radio emitters observed by SMaSH+ are all resolved, including the newly discovered pairs HD 168112 and CPD-47{deg}2963.