  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$$3\times10^{33}$ erg/s X-ray
luminosity mode, which, as shown in Archibald et al. (2014), exhibits coherent
X-ray pulsations. This emission is interspersed with frequent lower flux mode
intervals with $\approx$$5\times 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.
