We report on comprehensive investigations of Er3Al2 exhibiting a number of magnetic states. We observe three spontaneous antiferromagnetic transitions at 10, 14, and 24 K. Furthermore, our high-field magnetization and sound-velocity measurements reveal a number of crystal-electric-field (CEF) transitions. Additionally, the velocity of transverse acoustic waves shows a pronounced softening with decreasing temperature in the paramagnetic state. A CEF model that includes quadrupolar interactions explains the observed magnetic and elastic properties and provides a CEF scheme of Er3Al2. However, to explain some of the observations, a refined, more sophisticated model needs to be developed.