This work investigates the responses of the fully-depleted silicon-on-insulator (FD-SOI) Hall sensors to the three main types of irradiation ionization effects, including the total ionizing dose (TID), transient dose rate (TDR), and single event transient (SET) effects. Via 3D technology computer aided design (TCAD) simulations with insulator fixed charge, radiation, heavy ion, and galvanomagnetic transport models, the performances of the transient current, Hall voltage, sensitivity, efficiency, and offset voltage have been evaluated. For the TID effect, the Hall voltage and sensitivity of the sensor increase after irradiation, while the efficiency and offset voltage decrease. As for TDR and SET effects, when the energy deposited on the sensor during a nuclear explosion or heavy ion injection is small, the transient Hall voltage of the off-state sensor first decreases and then returns to the initial value. However, if the energy deposition is large, the transient Hall voltage first decreases, then increases to a peak value and decreases to a fixed value. The physical mechanisms that produce different trends in the transient Hall voltage have been analyzed in detail.