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We study optical phenomena in generic regular, magnetically charged, spherically symmetric black hole spacetimes arising from coupling of the Einstein gravity and nonlinear electrodynamics (NED) with the Maxwellian weak-field limit, where photons follow null geodesics of an effective geometry, directly reflecting the electromagnetic nonlinearity. We compare the motion of photons with that of massless neutrinos, which are not affected directly by nonlinearities of the non-Maxwellian electromagnetic field and follow null geodesics of the background spacetime. We determine shadows of such black holes, compare the time delays of photons and neutrinos moving in their field, and construct images of the Keplerian disks. We demonstrate that in the case of the "Maxwellian" NED black holes the optical phenomena give relevant signatures of the NED effects detectable by GRAVITY or the Event Horizon Telescope, but they are not strong enough to be excluded by recent observations as in the case of regular Bardeen black holes.