In magnetoelectric media, an electric field can induce a magnetization and a magnetic field can induce a polarization, while the system remains in thermal equilibrium. This effect requires that both space-inversion and time-reversal symmetry are broken. We present a comprehensive theory  for magnetoelectricity in magnetically ordered quasi-2D systems, where antiferromagnetic (AFM) order plays a central role. We define a Néel operator t that describes AFM order, in the same way a magnetization m reflects ferromagnetic (FM) order. While m is even under space inversion and odd under time reversal, t describes a toroidal moment that is odd under both symmetries. Thus m and t quantify complementary aspects of magnetic order in solids. In quasi-2D systems FM order can be attributed to dipolar equilibrium currents that give rise to a magnetization. In the same way, AFM order arises from quadrupolar currents that generate the toroidal moment. The electric-field-induced magnetization can then be attributed to the electric manipulation of the quadrupolar currents. Considering FM zincblende and AFM diamond structures, we obtain quantitative expressions for the magnetoelectric responses due to electric and magnetic fields that reveal explicitly the inherent duality of these responses required by thermodynamics. Magnetoelectricity is found to be sizable in quasi-2D hole systems, where moderate electric fields can induce a magnetic moment of one Bohr magneton per charge carrier. Our theory provides a broad framework for the manipulation of magnetic order by means of external fields.