Playing Shogun: Total War, I noticed the graphics; while the terrain is 3D, the units appear to be 2D (sprites from different angles). Could anyone explain why they appear like that?

It's a level of detail system based on impostors (google: "impostor rendering"). The units are 3d models when viewed close up, but in the distance it renders the 3d models out to 2d textures, and then draws those textures as 2d sprites in the world. This lets them greatly reduce the workload of the animation system and reduce their polygon/draw-call counts, as you can render a handful of 3d models for a whole squad (so that there's some variation in the men), and then render those handful of sprites a hundred times (each sprite being only ~2 triangles).

[size=2]So besides being able to reduce the workload on the system, are there any other advantages of 2D sprites in a 3D environment? Are there any games that use completely 2D sprites in a 3D environment[size=2]? (thinking strategy games)

Games that want 3D functionality but a charming or funny cartoony style often use 2D sprites in a 3D world.

Do most 3D engines offer the ability to put sprites in? Are there any keywords i should search for?

You should be able to do that with any engine, yes.

Even if it doesn't specifically advertise sprite support, all you need are textured quads, which would be fundamentally the same as drawing any other mesh.