Do normal modes of oscillation cause permanent deformation?
These are visco-elastic oscillations that cause virtually no permanent deformation.

Following the Tohoku 2011 earthquake, this gravimeter in Metsähovi, Finland, measured a radial oscillation mode amplitude of 0.06 mm. The Earth's radius is 6371 km. So the resulting strains would be extremely small.

All but the lowest radial mode decays after a few days because the energy of the oscillations gets converted to heat by dissipative processes.