----- I am not an ESL teacher -----
Although Barb_D gave a nice explanation on the difference of these words I think there are many situations in which these words are used as synonymies. That is why I prefer math to language.
In math, complement, supplement and (replement?) are the values which should be added to an angle in order to make it 90°, 180° and 360° respectively.
I am not sure of the word "replement", in Portuguese we say:
"complemento", "suplemento" and "replemento". But I couldn't find an English word for "replemento", which word would one use for it?