These characters all mean "to attack" or "to invade", but what are the differences between them? When should one be used and not the others?
it is hard to tell what they exactly mean without contexts, but i can give you a very general idea of these characters:
征 (zheng1) means 'wage war by travelling a long distance'. it is usually associated with a war with a very large scale in both space and time.
伐 (fa2) is just 'to wage war against', nothing more. in fact, among all five characters, only the original meaning of 伐 is directly related with war.
讨 (tao3), literally "to demand", means "to wage war demanding justice/punish the wrongdoers"
侵 (qin1) means “to invade" or "to encroach"
袭 (xi2) is usually associated with “sudden attack”.
As single characters they are only used in classical Chinese scripts, and their level of just decreases as has been listed before.
征 usually describes a war initiated by the emporor against local rebels/nomades.
伐 describes a war between emporors/kings/dukes because of various affairs political, marital, etc.
讨 describes a war initiated by a low class, sometimes a minister, against a high class. e.g.讨武曌檄文
侵 describes a war unfair without proper Casus Belli, typically strong kingdoms bullying weak kungdoms.
袭 describes a battle initiated when the opponent is unprepared.
攻 means to attack on a general sense.
Note: Meaning of characters can only help you to understand words, but since mandarin has gone through so many years, it does not have a rigid way of composing words from characters. And in classical Chinese, characters may have plural meanings, and character used for the same meaning changes with time.
although I'm a native speaker, I still can't tell you the difference between them. In fact they have the same meaning, maybe include some little difference.
we always use them as following method: 征伐, 征讨, 侵袭
but don't mind it. Chinese is not a strict language. for example, elevator and escalator,we just use one word to describe them:电梯 sometimes we also use 手扶梯 to specific the escalator. But nobody will be puzzle when you say elevator when you point to a escalator.