In the second work of this series, we explore the optimal search strategy for serendipitous and gravitational-wave-triggered target-of-opportunity observations of kilonovae and optical short-duration gamma-ray burst (sGRB) afterglows from binary neutron star (BNS) mergers, assuming that cosmological kilonovae are AT2017gfo-like (but with viewing-angle dependence) and that the properties of afterglows are consistent with those of cosmological sGRB afterglows. A one-day cadence serendipitous search strategy with an exposure time of ∼ 30 s can always achieve an optimal search strategy of kilonovae and afterglows for various survey projects. We show that the optimal detection rates of the kilonova-dominated (afterglow-dominated) events are ∼ 0.2/0.5/0.8/20 yr −1 (∼ 500/300/600/3000 yr −1 ) for ZTF/Mephisto/WFST/LSST, respectively. A better search strategy for SiTian is to increase the exposure time. SiTian can find ∼ 5(6000) yr −1 kilonova-dominated (afterglow-dominated) events. We predict abundant off-axis orphan afterglows may be recorded in the survey database although not been identified. For target-of-opportunity observations, we simulate the maximum BNS gravitational-wave (GW) detection rates, which are ∼ 27/210/1800/2.0 × 10 5 yr −1 , in the networks of 2nd/2.5th/3rd(Voyager)/3rd(ET&CE)-generation GW detectors. In the upcoming 2nd-generation networks, follow-up observations with a limiting magnitude of m limit 22 − 23 mag can discover all EM signals from BNS GW events. Among these detected GW events, ∼ 60% events (∼ 16 yr −1 ) can detect clear kilonova signals, while afterglow-dominated events would account for the other ∼ 40% events (∼ 11 yr −1 ). In the 2.5th-and 3rd(Voyager)-generation era, the critical magnitudes for the detection of EM emissions from all BNS GW events would be ∼ 23.5 mag and ∼ 25 mag, respectively. Foreseeable optical survey projects cannot detect all EM signals of GW events detected during the ET&CE era.