  We present realistic expectations for the number and properties of neutron
star binary mergers to be detected as multi-messenger sources during the
upcoming fourth observing run (O4) of the LIGO-Virgo-KAGRA gravitational wave
(GW) detectors, with the aim of providing guidance for the optimization of
observing strategies. Our predictions are based on a population synthesis model
which includes the GW signal-to-noise ratio, the kilonova (KN) optical and
near-infrared light curves, the relativistic jet gamma-ray burst (GRB) prompt
emission peak photon flux, and the afterglow light curves in radio, optical and
X-rays. Within our assumptions, the rate of GW events to be confidently
detected during O4 is $7.7^{+11.9}_{-5.7}$ yr$^{-1}$ (calendar year), 78% of
which will produce a KN, and a lower 52% will also produce a relativistic jet.
The typical depth of current optical electromagnetic search and follow up
strategies is still sufficient to detect most of the KNe in O4, but only for
the first night or two. The prospects for detecting relativistic jet emission
are not promising. While closer events (within z<0.02) will likely still have a
detectable cocoon shock breakout, most events will have their GRB emission
(both prompt and afterglow) missed unless seen under a favorably small viewing
angle. This reduces the fraction of events with detectable jets to 2% (prompt
emission, serendipitous) and 10% (afterglow, deep radio monitoring),
corresponding to detection rates of $0.17^{+0.26}_{-0.13}$ and
$0.78^{+1.21}_{-0.58}$ yr$^{-1}$, respectively. When considering a GW
sub-threshold search triggered by a GRB detection, our predicted rate of GW+GRB
prompt emission detections increases up to a more promising
$0.75^{+1.16}_{-0.55}$ yr$^{-1}$.
