The incommensurate magnetic structures and phase diagrams of multiferroics has been explored on the basis of accurate micromagnetic analysis taking into account the spin flexoelecric interaction (Lifshitz invariant). The objects of the study are BiFeO_3-like single crystals and epitaxial films grown on the substrates. The main control parameters are the magnetic field, the magnetic anisotropy, and the epitaxial strain in the case of films. We predict novel quasi-cycloidal structures induced by external magnetic field or by epitaxial strain in the BiFeO_3-films. Phase diagrams representing the regions of homogeneous magnetic states and incommensurate structures stability are constructed for the two essential geometries of magnetic field (magnetic field oriented parallel to the principal crystal axis C_3 and perpendicular to this direction C_3). It is shown that the direction of applied magnetic field substantially affects a set of magnetic phases, properties of incommensurate structures, character of phase transitions. Novel conical type of cycloidal ordering is revealed during the transition from incommensurate cycloidal structure into homogeneous magnetic state. Elaborated phase diagrams allow estimate appropriate combination of control parameters (magnetic field, magnetic anisotropy, exchange stiffness) required to the destruction of cycloidal ordering corresponding to the transition into homogeneous structure. The results show that the magnitude of critical magnetic field suppressing cycloid is lowered in multiferroics films comparing to single crystals, it can be also lowered by the selection of orientation of magnetic field. Our results can be useful for strain engineering of new multiferroic functional materials on demand. ; Comment: 14 pages, 10 figures