Antiferromagnets (AFMs) are presently considered as promising materials for applications in spintronics and random access memories due to the robustness of information stored in AFM state against perturbing magnetic fields (P. Wadley et al., Science 351, 587 (2016)). In this respect, AFM multiferroics maybe attractive alternatives for conventional AFMs as the coupling of magnetism with ferroelectricity (magnetoelectric effect) offers an elegant possibility of electric field control and switching of AFM domains. Here we report the results of comprehensive experimental and theoretical investigations of the quadratic magnetoelectric (ME) effect in single crystals and high-resistive ceramics of Pb(Fe1/2Nb1/2)O3 (PFN) and (1- x)Pb(Fe1/2Nb1/2)O3xPbTiO3 (PFNxPT). We are interested primarily in the temperature range of multiferroic phase, T < 150 K, where the ME coupling coefficient is extremely large (as compared to well-known multiferroic BiFeO3) and shows sign reversal at paramagnetic-to-antiferromagnetic phase transition. Moreover, we observe strong ME response nonlinearity in the AFM phase in the magnetic fields of only few kOe. To describe the temperature and magnetic field dependencies of the above unusual features of ME effect in PFN and PFN-xPT, we use simple phenomenological Landau approach which explains experimental data surprisingly well. Our ME measurements demonstrate that the electric field of only 20-25 kV/cm is able to switch the AFM domains and align them with ferroelectric ones even in PFN ceramic samples.