OMC-2 FIR 4 is one of the closest known young intermediate-mass protoclusters, located at a distance of 420 pc in Orion. This region is one of the few where the complete 500-2000 GHz spectrum has been observed with the heterodyne spectrometer HIFI on board the Herschel satellite, and unbiased spectral surveys at 0.8, 1, 2 and 3 mm have been obtained with the JCMT and IRAM 30-m telescopes. In order to investigate the morphology of this region, we used the IRAM Plateau de Bure Interferometer to image OMC-2 FIR 4 in the 2-mm continuum emission, as well as in DCO+(2-1), DCN(2-1), C34S(3-2), and several CH3OH lines. In addition, we analysed observations of the NH3(1,1) and (2,2) inversion transitions made with the Very Large Array of the NRAO. The resulting maps have an angular resolution which allows us to resolve structures of 5, equivalent to 2000 AU. Our observations reveal three spatially resolved sources within OMC-2 FIR 4, of one or several solar masses each, with hints of further unresolved substructure within them. Two of these sources have elongated shapes and are associated with dust continuum emission peaks, thus likely containing at least one molecular core each. One of them also displays radio continuum emission, which may be attributed to a young B3-B4 star that dominates the overall luminosity output of the region. The third source identified displays a DCO+(2-1) emission peak, and weak dust continuum emission. Its higher abundance of DCO+ relative to the other two regions suggests a lower temperature and therefore its possible association with either a younger low-mass protostar or a starless core. It may alternatively be part of the colder envelope of OMC-2 FIR 4. Our interferometric observations evidence the complexity of this region, where multiple cores, chemical differentiation and an ionised region all coexist within an area of only 10000 AU.