"Liquid refuse" or "Liquid waste"?

If you are referring to the liquids that are discharged from residential and commercial buildings that consist mostly of water along with other materials (human excretions, soap, fertilizers, etc.), the term waste water is most commonly used in the US.

This ngram indicates that it is now far more prevelant than liquid waste. Liquid refuse has very little usage.

If you are talking about other types of unwanted liquids, such as toxic chemicals,you probably have to look at the patterns in the industry you are reporting on. By sheer numbers, liquid refuse does not seem to be in general use.

Waste is more common than refuse in American English. In both cases you would use the singular, waste or refuse.

Probably a better word to use is...

effluent - a discharge of liquid waste, as from a factory or nuclear plant.

...also defined here as liquid waste flowing out of a factory, farm, [etc.,] or a household.

Although this may not be the particular term you're looking for, I thought I should mention that minorly contaminated water previously used for washing, such as that from sinks, baths, and showers, is specifically referred to as "greywater" (also "graywater", "grey water", "gray water").

Wiktionary defines it as "water that is not clean enough to be potable, such as having been used for washing, but not contaminated with fecal matter or other source of dangerous bacteria or dangerous or noxious materials."