"Ich müsste meine Hausaufgaben" and "Ich sollte ..." actually have different connotations in German, but do they have them in English as well?
I should do my homework, otherwise I was not allowed to go out.
"should" by itself never refers to the past. In this case, you would have to say "I had to" (here the speaker refers to a past action)
I should do my homework, otherwise I will get a bad grade tomorrow.

(here the speaker refers to a future action, consequence)
I would have to do my homework, before I can go out tonight.

(here the speaker refers to the allowance that it is necessary to do one's homework, otherwise going-out in a club or the like will be permitted by your parents.)
Do these examples really differ in English? I think in German you can differenciate them very well, so I just tried to translate my examples literally).