  As a long-term energy source, tidal heating in subsurface oceans of icy
satellites can influence their thermal, rotational, and orbital evolution, and
the sustainability of oceans. We present a new theoretical treatment for tidal
heating in thin subsurface oceans with overlying incompressible elastic shells
of arbitrary thickness. The stabilizing effect of an overlying shell damps
ocean tides, reducing tidal heating. This effect is more pronounced on
Enceladus than on Europa because the effective rigidity on a small body like
Enceladus is larger. For the range of likely shell and ocean thicknesses of
Enceladus and Europa, the thin shell approximation of Beuthe (2016) is
generally accurate to less than about 4%.The time-averaged surface distribution
of ocean tidal heating is distinct from that due to dissipation in the solid
shell, with higher dissipation near the equator and poles for eccentricity and
obliquity forcing respectively. This can lead to unique horizontal shell
thickness variations if the shell is conductive. The surface displacement
driven by eccentricity and obliquity forcing can have a phase lag relative to
the forcing tidal potential due to the delayed ocean response. For Europa and
Enceladus, eccentricity forcing generally produces greater tidal amplitudes due
to the large eccentricity values relative to the obliquity values. Despite the
small obliquity values, obliquity forcing generally produces larger phase lags
due to the generation of Rossby-Haurwitz waves. If Europa's shell and ocean are
respectively 10 and 100 km thick, the tide amplitude and phase lag are 26.5 m
and $<1$ degree for eccentricity forcing, and $<2.5$ m and $<18$ degrees for
obliquity forcing. Measurement of the obliquity phase lag (e.g. by Europa
Clipper) would provide a probe of ocean thickness
