The strength and dynamics of magnetoelastic coupling through the paramagnetic (PM) – antiferromagnetic (AFM) – ferrimagnetic (FIM) transitions in multiferroic hexagonal ErMnO3 have been investigated by Resonant Ultrasound Spectroscopy. Elastic stiffening by up to 2% below the PM – AFM transition at 80 K arises from biquadratic coupling between strain and the magnetic order parameter with relaxation times longer than ~10-6 s for the response of spins to changes in strain. In contrast with YMnO3, the PM – AFM transition in ErMnO3 is accompanied by a peak in acoustic loss immediately below the Néel point which is interpreted in terms of strain relaxation accompanying ordering of spins of Er3+ at 4b sites. Changes in the magnetic ordering scheme at the AFM – FIM transition near 3 K are accompanied by elastic softening of ~0.03 %. Poling of the low temperature ferrimagnetic structure round magnetic hysteresis loops is detected as small changes in elastic stiffness which arise due to the contribution of piezomagnetic and/or piezoelectric moduli. Contributions of piezoelectric moduli to acoustic resonance frequencies also permit changes in the configuration of ferroelectric domains to be detected in response both to cycling through this transition and to application of a magnetic field. A peak in acoustic loss in the vicinity of 250 K is attributed to strain-mediated pinning/freezing of some aspect of the domain microstructure with an activation energy of ~0.25-0.3 eV. A return to the original elastic properties on heating to temperatures above ~250 K is interpreted in terms of backswitching of domains to the configuration they had at the start. These observations confirm the existence of subtle variations in magnetoelastic coupling behaviour relating to both the magnetic order parameters and magnetic domain structures.