  We are carrying out a dense monitoring of the blazar OJ 287 with Swift since
late 2015 as part of our project MOMO (Multiwavelength Observations and
Modeling of OJ 287). This is the densest existing monitoring of OJ 287
involving X-ray and UV data. In this latest publication of a sequence, we
characterize the multiwavelength variability of OJ 287 based on >4000 Swift
single-wave-band data sets including archival data since 2005. A structure
function analysis reveals a characteristic timescale of ~5 days in the
optical-UV at epochs of low-level activity, and larger during outbursts. The
discrete correlation function shows zero lag between optical and UV, with tau =
0+-1 days at the epoch of densest cadence. During outbursts (in 2016/17 and
2020) the X-rays follow the UV with near-zero lags. However, during quiescence,
the delay is 7-18 days with X-rays leading or lagging, interpreted as due to a
different X-ray component dominated by inverse Compton emission. Scaling
relations are used to derive the characteristic length scales of broad-line
region and torus in OJ 287. A remarkable, symmetric UV--optical deep fade is
identified in late 2017, lasting for 2 months. We rule out occultation from the
passage of a dusty cloud and a model where the secondary black hole deflects
the jet between the primary and observer. We speculate about a temporary
dispersion or jet swing event in the core or in a bright quasi-stationary jet
feature. The deep fade reveals an additional, spatially distinct X-ray
component. The epoch 2020.9-2021.1 was searched for precursor flare activity
predicted by the binary black hole model of OJ 287.
