"Want" is direct and simple. Use this when you are definite and stating a fact. However, be aware that being direct may also sound rude and selfish. "Would like" is suitable for requests and wishes. It is indirect and polite because it expresses something imagined (subjunctive), not something factual and direct. For "I think", you could also use "perhaps", "it seems that", "in my opinion", "as I see it" and many other expressions. For "I feel", it sounds more emotionally-based if you don't want to use a cold and logical "I think". It's best to know how to use several expressions, as they do have subtle differences. Don't rely on just one phrase.

'Want' is much stronger than 'would like'. It is more polite to use 'would like'..

In American English "I want" and "I would like" mean the same thing. "I would like" is usually considered more polite as it is conditional and "I want" is present tense and it also portrays a stronger wanting for the object. Same goes for saying "I want to go there" or "I would like to go there" you will hear both ways and they both mean the exact same thing. As far as saying "I think" when expressing an opinion it is fine to do. I will say "I think" all the time and others don't, but it is still correct to use it that way.

I mean i every-day conversation the two mean the same thing, but if you want to be really grammatical "want" would be the present tense, and "would want" would be the past tense subjunctive, which talks about what you might have wanted in the past.

Good question, Sabrina.