most of time, all of them can be exchanged.
( Ms help's example is great ) let's try another angle to distinguish them! pay more attention to the specific situation and the unique meaning which other phrase don't have:
1. when you express " want, would like to do/have, consider", use "想", "我很困,想睡觉i am sleepy and would like to have sleep", "我想学中文 i would like to learn chinese"
2. when you descibe "you think so, in fact it's not" , use"以为", “我以为你说谎 i think John lies to me!( in fact John told the truth)”