The invert of a sewer pipe is the surface of the bottom arc within which the liquid flows. The invert elevation is the elevation of the lowest part of that arc. By strict dictionary definition, a gutter or the center of an inverted crown paved section could be called the invert of the road. The term may have come from canal work to which it would apply.
I would not apply the term to a pressure pipe such as a water main.
Since for a pipe to flow by gravity the invert must be sloped (neglecting the constant injection of water at head) the term invert elevation applies to one point in thelength of the pipe. Invert level implies an equal elevation surface or line, something that shouldn't exist in normal practice.