What are the differences between 触犯, 冒犯, and 得罪? Can you give some examples about their usage?
They are actually quite alike but the collocations and the usages are different.
触犯：go against; offend; violate
触犯众怒 to draw public wrath
触犯我的利益 to encroach on one’s interest
触犯法条 to violate the law
对您多有冒犯，请原谅 Sorry to offend you.
冒犯(您)了 Sorry to offend you.
得罪：to offend (the situation would be more serious)
多有得罪，请原谅 Sorry to offend you.
得罪(您)了 Sorry to offend you.
他做了很多得罪人的事儿 He did many offensive things.