Overhang is the most common term used for eaves, since it describes the physical aspect of the eave.
Soffit is a type of eave, which is a board underneath the extended edge of the roof. Using this building term is an alternative way to describe eaves.
The cornice is an architectural term for a type of eave, which provides function and aesthetics. Cornices are ornamental design moldings projecting horizontally from the roof.
Projection describes the edge of the roof, which is the overhang eave. Building codes use the term "projection" when referencing eaves.