Why are twin engine airliners more fuel efficient than three or four engine airliners?
Not a fully definitive answer, but a large part of the "efficiency" of an aircraft is drag and weight. Two (larger) round engines will have less surface causing drag than four smaller ones. In addition, each engine will add complexity to the aircraft (fire monitors, fuel piping, extra hydraulics) as well as necessitating duplication of things like thrust reverses, all of which add extra weight and sometimes drag.

So, all things being equal, one huge engine would be most "efficient". This would obviously be difficult, and impractical for most passenger jets, so when they will fit, without scraping the ground, two are used. If more thrust is needed, then they break it down into three or four.

(Note, the main reason 4 engines were used in the first place was for redundancy. At least one country's [US?] regulations stated that the aircraft must be capable of sustained flight, including climbing, with the loss of an engine. 2-1 = 50% thrust lost where as 4-1= only 25% loss, therefore requiring less reserve power)

*Edit note #2 

"Twin engine airliners tend to have more excess power" they climb faster may be relevant in terms of efficiency, but part of the reason a twin will usually have more reserve thrust is due to the redundancy "keep flying" rules described above.