Seismo-hydrogeodynamic effects (SHGEs) in groundwater level (pressure) variations in a range of periods from minutes to hours and days during local and teleseismic earthquakes were considered based on the data of precision observations in a deep piezometric well located in a seismically active region. With the use of the tidal analysis and frequency dependence of the barometric response of the water level, a static confined response of groundwater pressure in a range of periods from hours to the first tens of days was established. The annual water level trend was characterized by the seasonal function of a hydrostatic head change in the well. In the groundwater pressure, changes were detected due to several types of seismo-hydrogeodynamic effects: 1—the coseismic fluctuations during the first tens of seconds and minutes after the arrival of seismic waves from the earthquakes with magnitudes of 5.3–9.1 at epicentral distances of 80–700 km; 2—the supposed hydrogeodynamic precursors of the two strongest events; 3—the four types of variations under the vibration impact of seismic waves from Mw = 6.8–9.1 earthquakes at epicentral distances of 80–14,600 km. The dependence of the distinguished types of SHGEs on the earthquake parameters, the intensity of the seismic impact in the well area and the amplitude-frequency composition of seismic waves were considered.