They will test the fuck out of these two, and for some reason I didn't remember them that well.
Anyway all the dictionaries list 不由得 as the 2nd definition of 由不得, but we're going to disregard that because we think its stupid and not helpful, like when the dictionary starts telling me all confusing words also mean all other ones as a 3rd or 4th definition 到底，究竟, etc.
由不得 = not "up to" X - 这件事由不得你. This (matter) isn't up to you.
不由得 = can't help.
horrible dict example:
他看到那些蚂蟥，不由得身上发麻。 Seeing those leeches he couldn't help but feel grossed out.
So, nciku and my dict and other examples often have this type of sentence,
他说得这么透彻，不由得你不信服。 with the prominent feature being the 不 after the subject and before the verb. This is a known issue, and I will work it out one day, just be aware of it.
Lucking for the test you just need to remember that 由不得 has this "not up to you" sense, remember 由不得你, and you should be fine.