It is said that given roughly similar aerodynamic and engine technology that twin engine airliners are more fuel efficient than 3 or 4 engine airliners. Why is this? The twin engine airliners tend to have more excess power so I'm thinking that they can climb faster and fly higher, lowering the amount of time spent climbing (uses more fuel than cruise) and lowering fuel consumption during cruise. I suppose that fuel consumption is less while the engines are idling as well. Are there other factors that go into the 2 vs 3 vs 4 engine fuel consumption issue?
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.
Part of the reason is that large engines tend to be thermodynamically more efficient than small ones, and this isn't specific to any one type of engine.
Theoretical engine cycle is understood in terms of compressing, heating, expanding volumes of gas in an ideal environment. The closer the engine approximates to that environment the closer the engine can get to its ideal efficiency.
Relatively cool metal surfaces like combustion chamber walls, or pistons and cylinder liners, detract from this, so the further you can keep the gas from the metal, (i.e. the larger the engine) the more efficient (for the same theoretical cycle).
Off-topic, large marine diesels can exceed 50% thermodynamic efficiency while small diesels may reach 40% as seen here. The same table shows this applies to gas turbines too, comparing a 36 MW gas turbine (Trent, 39.8%) to a 2.20MW one (P&W PW127, 27%) but these are just example numbers, not a really fair comparison. (It would be nice to see like-for-like-but-bigger comparisons)
So larger engines tend to have higher thermodynamic efficiency, it just so happens you also need fewer of them.
I'm not sure if the twin engined aicraft are more fuel effecient compared to their four engined counterparts. Is there any hard data available?
In general, newer aircraft are more fuel effecient compared to older ones. See http://www.transportenvironment.org/sites/te/files/media/2005-12_nlr_aviation_fuel_efficiency.pdf. For example, the Boeing 747-8 first flown in 2011 is more fuel efficient compared to the 787-8 which flew first in 2009 while being less efficient compared to 787-9 (which flew in 2013). It is instructive to note that the 747-8 uses the same engines as 787-8.
We can say the twinjets are more efficient because of the engines used in them. Almost all the aircraft under development are twinjets, with the A380 being the last 4 engine aircraft to enter (commercial) service. These aircraft incorporate a number of recent advances in the field (like increased use of composites along with better engines), which makes them more fuel efficient.
So, there is no reason to say that twinjets will be more efficient than four engines aircraft, but are usually so because of various other developments, which are also equally applicable to the four engined types.
Note: See the References given in https://en.wikipedia.org/wiki/Fuel_economy_in_aircraft for comparison of fuel effeciencies of aircrafts.