建立: build up. The emphasis lies with the action, which was implied to have been taken by inferior power or from scratch. You can 建立 a nation because nation is something naturally formed from the root. 成立: form up. The emphasis lies with the form. You can 成立 a company because before you 成立 it, it simply did not exist. 设立: establish/set up. The emphasis lies with action, which was implied to have been taken by a superior power. You cannot 设立 a company, but only a subsidiary company（分公司） when you have a mother company already.

建立，是指抽象的和具体的意义兼备的事物。多指人际关系和标志性事物的出现，建立，既能表示能够看到，也能表示象征意义存在。 成立，是指一件正确事实，确凿事物，多指事实的正确或让机构组织的出现。只能表示实质而又能够看到或料到的事情。 设立，指条件预先给出，或者让一件具体事物出现。能够表示象征性的存在，也能表示能够看到的形象。但多为抽象名义或试用事物。

They are verbs. In Chinese, there is an object after a verb, and they have different objects. 建立 is more formal , we always say 建立国家，建立基地 成立 can say 成立公司，成立组织 设立 can say 设立机构 To be honest,成立 is similar to 设立, so if you cannot distinguish 成立 and 设立，you can use one of them in a same sentence，Chinese people can understand.

Here's another old italki post on a similar topic: https://www.italki.com/question/148037

两国在这几十年间建立了深厚的友谊。 这个公司/组织刚刚成立。 为了应对这些情况，我们设立了新的部门专门负责处理此类事物。