I've read in a few places that müssen is more strict than sollen, and sollen is used when someone orders you to do something. But what if it was a strict order but not a law? Something like:
Wir ___ nicht so laut sein, hat Mama gesagt.
In this sentence should we use sollen because it's an order, or use müssen because it's strict?
The example doesn't work because in a phrase of the form
nicht X müssen
nicht negates the modal verb, not X, thereby indicating the absence of an obligation (and not the obligation to refrain from X). Consequently, the following utterance is infelicitous:
Wir müssen nicht laut sein.
We are not required to be loud.
Without the negation, the difference between
Wir müssen leise sein.
Wir sollen leise sein.
isn't about strictness, but about the source of the obligation: sollen clearly indicates that a third person, not the speaker, is the source of the obligation (whereas müssen doesn't say anything about the source of the obligation).
A third option would be the past subjunctive of sollen, which indicates that being silent is not an obligation, but a good idea or something that would be well received.
Wir sollten leise sein.
Yes as a rule of thumb "müssen" is more of an imperative order, while "sollen" is more of a guideline. But similar to must, must not, have to, don't have to and need to, don't need to, should and shouldn't there are also combinations where it's a little more nuanced.
So "wir müssen nicht so laut sein", implies that you'd otherwise be required to scream above a certain loudness but today are given a day off from your screaming duty so you don't have to be that loud. So the guideline version would be "wir sollen nicht so laut sein", implying that mama told them to be as quite as possible. If you want to make it more imperative than you'd rather use "we're not allowed to be so loud" = "wir dürfen nicht so laut sein...", implying that cruel and unusual punishment like earlier bedtime would be the consequence.
This is one of the things you notice when you visit England for the first time as a German person: 'Must not' does not mean 'nicht müssen' and not even 'nicht sollen' - but 'nicht dürfen'.
