Imperative means required. Compulsory and mandatory are other synonyms. Momentous and pivotal mean important, but can also imply that the things they describe have caused changes. Crucial means extremely important. Another synonym is key.

I would say the difference between most of them is a level of magnatude. Particularly between Important, Imperative, and Crucial. Example: In working out your budget with your pay from work, it is Important to put some money aside for a savings funds, but it is crucial to pay for your rent first. To me, this would mean that while saving money is important, but paying for somewhere to live has the priority, it is *more* important.

Important, imperative, and crucial can been seen as three levels of importance. Important, very important, and of absolute importance (these levels can also be correlated with urgency in any given situation). Pivotal and momentous are used to describe an important effect or reaction to a change. A pivotal moment could change the course of a life path. Or, a momentous moment could influence the course of a life path, but not change it.

What is important is to know the exact meaning of each word and how it is used. If you just learn synonyms, you will have problems in knowing the nuances and may use the wrong words.