LIke most simliar but distinct verbs -- the difference is not in meaning, its in HOW THEY ARE USED i.e. the full meaning (full power) of the verb is made clearer when a verb is combined with a noun (a collocation)
to defy the authorities
The protesters defied the authorities and now they are in jail.
to breach protocol
When you're talking to the President, follow the rules and don't breach protocol (=the proper procedures)
to breach the walls
Genghis Khan was able to breach the walls of the city with a battering ram.
to violate customs
When is Rome, do as the Romans -- don't violate the customs of the local people.
to violate privacy
The NSA has violated the privacy of ... everyone in the world?
brutally violate / a brutal violation
The actions of the NSA are a brutal (=extreme, hard) violation of the 4th Amendment of the US Constitution.
The actions of the NSA are a flagrant (clear, obvious) violation of the 4th Amendment.
to break the rules
If you break traffic rules in Toronto, the fines are high.
to break (down) the barriers
Learning multiple languages breaks down barriers between peoples and cultures
to break (up) a relationship
"Honey, it's not you, it's me..."
to break (up) a fight
The police were called to break up the fighting between the drunk football fans
The best way to learn these is a printed collocations dictionary like this one http://www.amazon.com/Longman-Collocations-Dictionary-Thesaurus-Online/dp/1408252260 (maybe at your university library???)
I haven't found an online dictionary / database that is really user-friendly.
You can use corpus databases to research collocations but they're not user-friendly. This site gives you basic collocations for most verbs: http://www.ozdic.com/collocation-dictionary/violate
Working with how verbs are used i.e. collocations (rather than "What do they mean?") is a way to traverse that "intermediate plateau" ...