Two-dimensional (2D) ferromagnetic and ferroelectric materials attract unprecedented attention due to the spontaneous-symmetry-breaking induced novel properties and multifarious potential applications. Here we systematically investigate a large family (148) of 2D MGeX₃ (M = metal elements, X = O/S/Se/Te) by means of the high-throughput first-principles calculations, and focus on their possible ferroic properties including ferromagnetism, ferroelectricity, and ferroelasticity. We discover eight stable 2D ferromagnets including five semiconductors and three half-metals, 21 2D antiferromagnets, and 11 stable 2D ferroelectric semiconductors including two multiferroic materials. Particularly, MnGeSe₃ and MnGeTe₃ are predicted to be room-temperature 2D ferromagnetic half metals with T_c of 490 and 308 K, respectively. It is probably for the first time that ferroelectricity is uncovered in 2D MGeX₃ family, which derives from the spontaneous symmetry breaking induced by unexpected displacements of Ge-Ge atomic pairs, and we also reveal that the electric polarizations are in proportion to the ratio of electronegativity of X and M atoms, and IVB group metal elements are highly favored for 2D ferroelectricity. Magnetic tunnel junction and water-splitting photocatalyst based on 2D ferroic MGeX₃ are proposed as examples of wide potential applications. The atlas of ferroicity in 2D MGeX_{3 ­}materials will spur great interest in experimental studies and would lead to diverse applications.