These words mean to make or to become smaller or less.
Reduce is the most general among these words and is used in a variety of situations. It means to bring down to a smaller extent, size, amount, number, etc. It may also suggest lowering in degree or intensity. Further it may mean to bring down to a lower rank, dignity, etc.
Abate usually means to reduce something which is widespread or extremely intense.
Ex – The storm has abated.
In law it means to remove completely – to abate a nuisance.
Curtail suggests sudden and abrupt shortening. It may also mean to place a restriction on something. The word is usually used only for nonmaterial things.
Ex – Our holiday was curtailed due to an emergency in office.
Diminish suggests progressive lessening but not to the point of total disappearance.
Ex – My eyesight has diminished with age.