I don't think there is any really reliable cross-linguistic labelling system that would include all of these. There are terms for most of them, but they're often used for only a few languages, and perhaps not very consistently. For someone who is created a conlang, they have flexibility then to adapt these terms for their language, however the important thing is to clearly describe in detail the full semantics of the language, rather than just assigning labels.
The broad category for all of these is deontic modality, which covers the modality of how the speaker thinks things ought to be. Within deontic modality there are many subtypes. The SIL Glossary has a very useful section giving a hierarchical description of deontic modality.
English actually has a very large number of modal verbs, with subtly different senses, so with examples from English we can illustrate a lot of the subtypes, even though they're usually not given clear labels. The English modals are however very complex, most of them being used in different contexts to mean very different things.
The imperative is actually one of the least marked ways of issuing a directive/command. In English it is a structurally different way of forming a sentence, but in other languages it may have a more regular structure with a particular verb form that fits into a wider affix paradigm.
Should is usually weaker than the imperative, giving a recommendation. Possible labels include hortative and propositive.
Have to, need to and must can all be stronger than the imperative, but they also often imply that the person giving the instruction needs to plead to some extent with those they are instructing; an autocratic dictator would never tell their servants that they need to do something, they would simply tell them to do it (with an imperative sentence.) Labels include precative for requests, and directive and obligative for commands that emphasise obligation.
When will or shall are emphasised and stressed in English they are used to indicate a serious instruction, which sometimes sound almost sinister with an implied threat for those who disregard them: "You will do this... (or else!)" The label commissive is used for threats, but not exclusively, as it's also used for promises.