Good question :)
I never really thought about it, but...
Angry and furious are much the same, except furious is *alot* stronger.
Annoyed is similar to angry but can also be very temporary; someone in line at the bank might annoy you if they're talking on their phone loudly but once you leave the bank, you forget about it and are fine. :)
Cross isn't used much in American English but as I understand it, it's the same as mad (angry) -hey that's another one, you forgot "mad", hehe. There are more just likes these, but it's a good start.
Any other questions, let me know. :)