The use of OSB for interior wall surfaces is a non-standard practice and maybe in violation of some building codes. Installing a plaster surface onto OSB is difficult and usually requires some special adhesives and techniques in order to function. For exampe, it might require the application of a mesh on all the surfaces in order to compensate for the natural movement in the wood.
As you have described it, the failure of the plaster surfaces shows that this interior wall surface was installed in a sub-standard manner - does not meet minimum practices of the trades. It has failed preternaturally and partial repairs are unlikely to produce a lasting result. It maybe possible to remove all of the plaster material (drywall mud or whatever) clean the OSB surface, apply an adhesive primer/base and then apply a new plaster surface. The cost of such repairs are most likely going to be much higher than the removal of the OSB and the installation of a drywall surface. It might be possible to leave the OSB on the walls in areas of cabinets etc. but even that will depend upon applicable codes.<