The PSR J1023+0038 binary system hosts a neutron star and a low-mass, main-sequence-like star. It switches on year timescales between states as an eclipsing radio millisecond pulsar and a low-mass X-ray binary. We present a multi-wavelength observational campaign of PSR J1023+0038 in its most recent low-mass X-ray binary state. Two long XMM-Newton observations reveal that the system spends ~70% of the time in a $approx$$3times10^{33}$ erg/s X-ray luminosity mode, which, as shown in Archibald et al. (2014), exhibits coherent X-ray pulsations. This emission is interspersed with frequent lower flux mode intervals with $approx$$5times 10^{32}$ erg/s and sporadic flares reaching up to $approx$$10^{34}$ erg/s, with neither mode showing significant X-ray pulsations. The switches between the three flux modes occur on timescales of order 10 s. In the UV and optical, we observe occasional intense flares coincident with those observed in X-rays. Our radio timing observations reveal no pulsations at the pulsar period during any of the three X-ray modes, presumably due to complete quenching of the radio emission mechanism by the accretion flow. Radio imaging detects highly variable, flat-spectrum continuum emission from PSR J1023+0038, consistent with an origin in a weak jet-like outflow. Our concurrent X-ray and radio continuum data sets do not exhibit any correlated behavior. The observational evidence we present bears qualitative resemblance to the behavior predicted by some existing propeller and trapped disk accretion models although none can fully account for all aspects of the rich phenomenology of this system.
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