Reading through Wikipedia says that Coriolis was the first to introduce the notion of work, described as "weight lifted through a height".
Our modern conception of work is of a force that realizes a displacement. This is general and valid for most forces (I don't know if we can apply this in general relativity or quantum mechanics). The book I'm studying for thermodynamics says that Joule's experiments clarified the relationship between heat and work, moving on to the first law.
We now regard heat as energy and give it his name. I don't think they saw these concepts in the same light we do now. Energy is one of the fundamental principles all of physics is based on, and it has many faces: Vibrational, kinetic (translational and rotational), heat, potential, internal energy, etc. When did work and energy they take the form we use now?
The book is "Mere Thermodynamics", by Don Lemons.