Based on our dedicated Swift monitoring program, MOMO, OJ 287 is one of the best-monitored blazars in the X-ray-UV-optical regime. Here, we report results from our accompanying, dense, multifrequency (1.4-44GHz) radio monitoring of OJ 287 between 2015 and 2022 covering a broad range of activity states. Fermi {gamma}-ray observations were added. We characterize the radio flux and spectral variability in detail, including discrete correlation function and other variability analyses, and discuss its connection with the multiwavelength emission. Deep fades of the radio and optical-UV fluxes are found to occur every 1-2 yr. Further, it is shown that a precursor flare of thermal bremsstrahlung predicted by one of the binary supermassive black hole (SMBH) models of OJ 287 was absent. We then focus on the nature of the extraordinary, nonthermal, 2016/2017 outburst that we initially discovered with Swift. We interpret it as the latest of the famous optical double-peaked outbursts of OJ 287, favoring binary scenarios that do not require a highly precessing secondary SMBH.