In this sentence I can't figure out why it's "lass" not "lassen":
Lass uns am Samstagabend ausgehen.
Also, if the subject is "uns" why it's not in the nominative case?
The sentence is in imperative form. Imperative sentences usually have no explicit subject. Your sentence translates to English:
Let's go out on Saturday night
Looking at that it follows the exact same grammatical pattern with only slightly different word order.
If you would want to make a simple statement, yes, then it would read differently with a proper subject "wir" and no form of "lassen" (English 'let') because there is no one from whom we need permission:
Wir gehen am Samstag Abend aus.
But that's different in English, too: We go out on Saturday night.
The subject of that sentence is du. But it's not posted because lass is second person singular imperative mood. The subject can't be anything else but du. You may argue that German doesn't drop pronouns usually, but this is an exception. Also, in colloquial speech pronouns are often dropped in German.
Uns is in accusative case because it's the object to lassen. It tells who is let. It doesn't tell who lets. That's du.
Be careful however:
This adresses a single person in the familiar way. (“du”)
This adresses a group of persons in the familiar way. (“ihr”)
This addresses a single person or a group of persons in the distant way. (“Sie”) It's not in imperative mood but instead it's third person plural, posts the subject Sie (also mind the caps!) and has no topic in front so it looks similar to an imperative mood clause.
The tricky part is that they all mean the same: Let (you) us go out on saturday night. It's just different persons addressed in different ways.