effective, effectual, efficacious, efficient
1. All these words mean ‘having an effect’ of some kind, but with different applications and shades of meaning. Effective means ‘having a definite or desired effect’ that is actual rather than theoretical:

• The toothbrush is undoubtedly the most effective weapon in the fight against bacterial plaque —Daily Telegraph, 1971

• She is most effective as a live performer of her own material —New Yorker, 1975

• Referring fracture patients for a DXA scan has been effective in helping prevent further breaks —Scotsman, 2007.

Cost-effective means ‘productive in terms of cost’. Effectual means ‘capable of producing the required result or effect’, independent of a personal agent, and is often more theoretical than actual:

• The rich ought to have an effectual barrier in the constitution against being robbed, plundered, and murdered, as well as the poor —A. Arblaster, 1987

• The rim of my hat, while effectually shading my eyes, did not obstruct my vision —J. Davidson, 1991.

A person cannot be described as effectual although he or she can be described as ineffectual, i.e. ‘lacking the ability to produce results’:

• The Rangers' problems stemmed from the habit that…the team's general manager…had of hiring ineffectual cronies to coach the club —New York Times, 1979.

2. Efficacious applies only to things, and means ‘producing or sure to produce the required effect’:

• It is perhaps dubious to argue that a prayer or worship becomes more efficacious if more people join in —S. Lamont, 1989

• How can I persuade them, when they go to the bar, that a Perrier or a tonic water might be just as efficacious as alcoholic liquor? —S. J. Carne, 1990.

Efficient refers to a person's or thing's capacity to do work and produce results with minimum effort and cost:

• You police spies don't seem to be a very efficient bunch, letting an old man be drowned while you are supposed to be keeping a watch on him —G. Sims, 1973

• Older systems can be improved with modern, efficient components and controls can be added to improve fuel economy —Ideal Home, 1991.

In recent use, efficient is sometimes preceded by an attributive noun that defines the scope of the efficiency, notably in relation to energy:

• Flights can be ‘offset’, which means you work out your carbon emissions and then send money to fund tree planting or energy efficient technologies —Daily Mail, 2007.

Modern English usage. 2014.