Both run away and run off mean escape, but is there any difference?
Run away means you put distance between yourself and the unpleasant thing. It doesn't say whether your escape was successful. It doesn't say whether you're coming back. It doesn't say whether anyone will catch up with you.
Run off means you went somewhere that you cannot be effectively retrieved either because you went someplace hard to reach or because no one knows where you went. It usually implies that you're not coming back. "Run off" can almost always be changed to "run away" without making a statement false.
A specific use of "run away" is actually closer to the meaning of "run off", and that is when a child or teenager runs away from their parents for a long period of time (days, months, years or permanently). The child or teenager is said to be "running away from home" and is referred to as a "runaway".
http://www.merriam-webster.com/dictionary/run%20off gives another usage of "run off".
Run off can refer to causing someone else to run off.
- "I ran off the intruder by chasing him and throwing rocks at him".
- "The intruder ran off when I chased him and threw rocks at him".
Both sentence are good and mean pretty much the same thing.
To run away is to escape an undesirable situation with the usual implication of not coming back
run away from the burning building
The run aways left home by bus
The dish ran away with the spoon
it can also mean out of control
the run away train
but because something is running away it does not necessarily mean it will get away
they ran away from the police but were caught before they got away in their get away car
To get away is to successful evade (usually) capture
he got away from the law
We will get away for the weekend by running away without the kids
it can also mean a vacation or holiday
a quick get away to a foreign country
tropical island get away
Take some time off and get away from it all
If you run away it does not mean you will get away, but if you get away it means you successfully ran away
One usually will run off with someone or something in a sudden manner
she ran off with her boyfriend before anyone noticed
he ran off with the goods when no one was looking
If you run away it is best to run off and not delay, or you might get caught and not be able to get away from whatever is chasing you.
That's quite a tricky question as I found out. As a non-native I had to consult Oald. They have an entry for to run off with, saying that to run away with and to run off with are interchangeable.
There is also an entry for to run off with special meanings.See BrE and AmE.