English has three modals for deontic differences. Ranked from lest to most obligatory, they seem to be:
cf. «What is the difference between “have to”, “must”, and “should”?»
Would this be the proper Italian ranking from least to most obligatory?:
Simply put, there is no ranking in Italian. There is a single verb, dovere, which can be declined in the various tenses to put the action somewhere in the time, or used in conditional tense to express a doubt. In this case, the condizionale can slightly vary or weaken the whole sentence, so I think that the ranking you ask for could roughly be this:
He should < He has to < He must.
dovrebbe < ?? < deve
As stated in the other answer, the "dovrebbe" is not really a weaker form of "dovere", but instead a doubt about the trueness of the outcome: you should be careful when using "dovrebbe".
You mentioned "debba", which is simply a subjunctive of "dovere", and it is used (hopefully) just like the italian grammar says, but it has nothing to do with graduality or strongness of "dovere".
Here are some examples:
Devo andare (I must go)
Ho da andare ("I have to go", but it means "I must go")
Dovrei andare (I must go (but I can't / I won't))
Some examples with more context:
Quando pigio il pulsante, la luce deve accendersi
= When I press the button, the light must turn on
Quando pigio il pulsante, la luce dovrebbe accendersi
= I expect that when I press the button, the light turns on, but I am not really sure - maybe the button is broken, or the lamp is burned?
Sei sicuro che, pigiando il pulsante, la luce debba accendersi?
= Are you sure that, when pressing the button, the light has to turn on?
In this last phrase, the "debba" is used because the grammar requests it, but there is no implication about the strongness of "dovere", the whole doubt is about the correlation between the button and the light, not about the behavior of the light itself.
