these are all modal verbs, but thier functions differ.
'I should do that' implies the speaker is aware of what is best, yet not necessarilly willing to do what it is that they 'should'.
'I would do that' is written in the subjunctive mood. The simple sentence is likely to be joined to a subordinate adverbial clause, initiated with 'if', for instance, 'I would do that if I had the time'. So 'would' is used to express condition (what may have been done under diffrrent circumstances)
'I could do that' expresses possibility. It is not epistemic, thus it does not convey certainty, but instead reveals an option. this is where thev witticism; (Student) 'can i go the toilet?' (Teacher) 'I'm sure you could, but I'm not going to let you!' comes from
'Must' is epistemic, thus implies certainty. 'You must do it'. The request is not optional (as it would be if the 'must' was replaced by 'could').
'might' conveys uncertainty. It is a possibility. 'I might go swimming tomorrow'. the speaker is currently undecided.