OXFORD DICTIONARY
should, v.aux. (3rd sing. should) past of SHALL, used esp.:
1 in reported speech, esp. with the reported element in the 1st person (I said I should be home by evening).
Cf. WILL(1), WOULD, now more common in this sense, esp. to avoid implications of sense 2.
2 a to express a duty, obligation, or likelihood; = OUGHT(1) (I should tell you; you should have been more careful; they should have arrived by now). b (in the 1st person) to express a tentative suggestion (I should like to say something).
3 a expressing the conditional mood in the 1st person (cf. WOULD) (I should have been killed if I had gone). b forming a conditional protasis or indefinite clause (if you should see him; should they arrive, tell them where to go).
4 expressing purpose = MAY, MIGHT(1) (in order that we should not worry).
THESAURUS
should
be expedient, be forced, be in for, be necessary, be obliged, cannot do otherwise, cannot help but, had best, had better, have got to, have need to, have to, must, need, need to, needs must, ought, ought to