keep on 是坚持,保持,克服困难继续坚持,不要停顿。
例：I wish you wouldn't keep on about the coat you want to buy．我希望你不要再唠叨那件你想买的外套了。
go on 是很随意的坚持,继续就好的意思,可以中间有停顿 go on to do sth或者没有停顿 go on doing sth
例：I'd like to go on a long triP away from these troubles．我要去作一次很远的旅行，以摆脱这些烦恼。
keep on doing和keep doing都是说继续做.但两者存在微妙的区别。
keep on doing是指中间有休息停顿的不停地做
比如keep on reading,并不是说一直不停地读书,这期间可以停顿或者已经休息过了等。
而keep doing是指持续不...
continue sth或continue with sth译为：(在停止后）继续..
He continued went on with the story.
他继续讲这个故事。
continue to do和continue doing，都译为“不停地…继续做..”的意思。
They contiuned talking after the meal.
吃了饭后他们又继续谈。
continue作不及物动词时，后常接adj/prep短语做表语=remain
He picked up his book and continued reading.
他拿起书继续读下去。
continue 译为“继续说接着说”
“And so” he continued,“we will try harder next time.
“所以”他继续说，“下次我们会更努力的。”。