Within the entire gamut of magnetostrictive, piezomagnetic, and ferromagnetic shape memory alloy systems, the striction effect is found to vary from a few tens of parts per million to a few percent. Here, we report the observation of an unprecedentedly large magnetic-field-induced lattice strain along the c axis (more than 60-100% at 90 kOe field) in single crystals of orthorhombic RFeO₃ (R = Dy, Ho) below their spin-reorientation transition temperature T_SR. However, the striction effect is two orders of magnitude smaller along the a and b axes. Like magnetostriction, the magnetodielectric effect is highly anisotropic and very large along the c axis. Such gigantic striction and dielectric effects along the c axis arise as a result of a magnetic-field-induced first-order structural phase transition which possibly stems from large spin-orbit coupling (and, thereby, enormous magnetocrystalline anisotropy). The observed colossal striction in rare-earth orthoferrites could open new opportunities for applications requiring large, reversible magnetic-field-induced strain.