MONOS: Multiplicity Of Northern O-type Spectroscopic systems. I. Project description and spectral classifications and visual multiplicity of previously known objects

[ABRIDGED] AIMS. MONOS is collecting information and studying O-type spectroscopic binaries with delta > -20 deg. In this 1st paper we describe the sample and provide spectral classifications and additional information for objects with previous SB or EB orbits. In the future we will test the validity of previous solutions and calculate new SB orbits. METHODS.The spectra in this paper have 2 sources: GOSSS, which is obtaining blue-violet R~2500 spectroscopy of thousands of massive stars, and LiLiMaRlin, a library of libraries of high-resolution spectroscopy of massive stars obtained from 4 different surveys and additional data from our own observing programs and public archives. We also use lucky images from AstraLux. RESULTS. We present homogeneous spectral classifications for 92 O-type spectroscopic multiple systems and 10 optical companions. We discuss the visual multiplicity of each system with the support of AstraLux images and additional sources. For 11 O-type objects and for 6 B-type objects we present their first GOSSS spectral classifications. For 2 known EBs we detect SB2/SB1 lines for the first time, to which we add a third system already reported by us recently. For 2 previous SB1 systems we detect their SB2 nature for the first time and give their first separate spectral classifications, something we also do for a 3rd object just recently identified as a SB2. We also detect 9 new astrometric companions and provide updated information on several others. For sigma Ori AaAbB we provide spectral classifications for the 3 components with a single observation for the first time thanks to a lucky spectroscopy observation obtained close to the Aa,Ab periastron and for theta^1 Ori CaCb we add it to the class of Galactic Of?p stars, raising the number of its members to 6. Our sample of O-type spectroscopic binaries contains more triple/higher-order systems than double systems.