I would like to try. 1)愿意 : it's often used in a language situation of taking or giving advice.Besides, it's quite formal,and usually used when you make an important decision. e.g. would you like to join my wedding ? yes, I'd like to. 2)想: =want to without preconditions, it emphasizes the things you wanna do. I can be an instant idea or a careful consideration.But, it's usually not formal. e.g. I wanna eat an icecream. or The boy wants to become a philosopher in the future. 3)要: also equal to "want to", but it is entered into a bit tone of order,and the things you want to are those you have decided to. The expression is stronger than 想 e.g. I told her to dry up. 我要他住嘴. In addtion, "要"also means "get" or "take". e.g. This one is better, i take it. 这个更好点,我要了. 4)应该 : following some ethics , principle or rules ,you should do or you must to. e.g. You should act in conformity with the rules. You should eat up your food. 5)得: =应该 It is the oral language.

you have known the meaning of them,so here i only tell their emphasis: 愿意：be glad to ,be like to do sth 想：just want to,may be not do.eg:我想去北京。（我有这个想法，但是还没行动） 要：want to and maybe you will do it soon.eg:我要去北京。（有这个想法，说不定已经打算好了，有时候语境不同，还表示马上就要走了） 应该：should do,that's your obligation,wether u like or not.eg:你不应该替他写作业。（你没有这个义务） 得： 得=应该，and it's informal and colloquial.

愿意and想,they are the same 应该means you have to ,but may be you don't want it that way 要means you feel like something.Such as you go to a Chinese reasturant,you say to a waiter:我要一杯咖啡。

“wants” is you likes doing this matter. For instance, you are willing to climb a mountain together with me? You said: I want! “thinks”, is your thought control you are handling anything. For instance you want to go to eat meal. “wants”, wants any thing, here “thing” including many. For instance: “I want you to take down that thing. I ask for money.”Many! I replied your question you can help me to take the English name? My Chinese named Huang Kun.

愿意 vs 想 要 In most situatiion, when you say"我愿意", it means you have made a decision and will not regret for this decision. For example, your boyfriend propose to you, you can say "我愿意" to accept his proposal. 想 and 要 share the same meanings of "want to". you can just put them together to say 想要 as well. 愿意 expresses someone's decision, while 想 and 要 express someone's intention. For example, if you want to get married, you can say "我想結婚". However, 想 has another meanings such as "think", "to miss someone", and 要 aslo has another meaning "have to". They are different.