Most efficient leveling outside MSQ.

[AmiableApkallu]

I don't know what's "most efficient", but for me, "simple and reliable" is:

• Daily roulettes: Each roulette gives a sizable EXP bonus once per day. The Frontlines roulette gives the EXP to the PvE job you queue as, so you can switch to your preferred PvP job once you're in the instance.
  
• Highest level dungeon you can queue for that isn't Lv. 50/60/70/….
  
• Weekly challenge log.
  

[Powercow]

I don't know what's "most efficient", but for me, "simple and reliable" is:

• Daily roulettes: Each roulette gives a sizable EXP bonus once per day. The Frontlines roulette gives the EXP to the PvE job you queue as, so you can switch to your preferred PvP job once you're in the instance.
  
• Highest level dungeon you can queue for that isn't Lv. 50/60/70/….
  
• Weekly challenge log.
  

This guy's got the right idea, but I would add in the caveat that only Leveling, MSQ, and Frontlines roulettes are good and time efficient. Guildhest roulette, alliance raid roulette, and 50/60/70/80 roulettes just don't give enough EXP over running another dungeon of your highest level. They're not horribly inefficient though, if you just want a change of pace.

In between queue pops (definitely more of an issue with DPS than healer or tank), either take a break and goof around in the Gold Saucer or with crafting, if you don't want to risk any kind of burnout. If you really want to power level though, knock out the highest level FATEs you can, and do your current expansion's hunts as you're able to (i.e. pick up all the hunt pages, then do FATES and hunt targets in your zone.) Don't underestimate the power of the challenge log -- those continue to scale with good EXP up until the current expansion (so they stop scaling at 79, they're still good EXP all the way though.)

Oh, and be sure to pick up the Wondrous Tails from Khloe in Idyllshire. Completing 9 stamps gives 50% of a level's worth of EXP once a week, and it should only take a couple of Second Chance resets to get all 9. Plus, that and MSQ Roulette will make sure you're well-stocked on poetics so you can keep your gear up to date for all your alt jobs.

Edit-
Oh, forgot to mention. Do 3 "Under the Armor" guildhests (it's the second one) per week, just for the challenge log. Each run takes like 60 seconds (half of which is loading in and out) and the challenge log bonus is quite good. Also give people commendations for that challenge log too.