Squirrels spend most of their summer getting ready for the winter. They gather nuts and hide them away so that they can eat them when food becomes scarce. So, when you say that someone has `squirreled something away’, what you mean is that he has hidden or stored something away in order to use it later on.
Example: I’m told that Rajesh has been squirreling away money for several years now.
When you succeed in `squirreling out of something’, you manage to escape doing what you were supposed to do. You get out of a situation you do not wish to be in.
Examples: *Babu will do anything he can to squirrel out of going to the dentist. *Listen to me! You have to do it. Don’t you dare try to squirrel out of it.