escape

逃れる(のがれる) To escape through luck (escape the death penalty/ there was an earthquake but my house escaped damage) .
 
逃げる(にげる) To run away, to escape on purpose.   $$$
 
避ける(さける) To dodge (a bullet, a kick) (can be used figuratively)
 
免れる(まぬかれる) To get out of (your punishment, because you had a good excuse), get out of paying a fine (because you are related to the Chief of Police). To be exempt from. 免れる can also sometimes be used like 逃れる – to escape misfortune through luck.
 
脱出(だっしゅつ) To escape from prison, escape from the POW camp like Rambo. escape from North Korea. . . but you can also use it like, “He escaped from the crisis.” Or, “She escaped from the wreckage of the crashed airplane.”
 
退く(しりぞく) Withdraw (from competition, troops withdraw from the Gaza strip, sometimes also means retire).