Two-dimensional (2D) intrinsic ferromagnets with high magnetic anisotropy at room temperature are crucial for ultra-thin spintronic applications. Here, we reveal that monolayer Fe2CoGaTe2 is stable and exhibits giant perpendicular magnetic anisotropy energy (MAE = 4.78 meV) together with a high Curie temperature (TC = 340 K). Its MAE exceeds that of known 2D ferromagnets by an order of magnitude. Remarkably, strain engineering enables both MAE reversal and increased TC, which stem from the strain-induced redistribution of Te orbital contributions and an enhanced cumulative exchange coefficient. Our results establish monolayer Fe2CoGaTe2 as a highly promising 2D room-temperature ferromagnet and elucidate the strain-induced mechanisms underlying MAE switching and TC enhancement, providing valuable guidance for the development of strain-engineerable spintronic devices.