Difference between "Let us go" and "Let we go"?

Just wanted to know the correct usage of 'us' and 'we' .

Are there any contexts in which they can be used interchangeably?

I know "Let we go" seems wrong..but couldn't explain it.

Us is accusative since it is the direct object of let. Disambiguation might help:

Allow us to go.

The convention is to delete the to from the verb after let; otherwise it is the same as allow:

Allow them to come here turns into Let them come here.

Let is followed from the object, which is then us, not we; we is used in the subject case, while us is used in the object case.

My boss let me leave early.
"Dear God," Jessica prayed, "let him be all right."

In your examples, 'let' is imperative (or hortatory, I suppose, but I think it's classed as the imperative mood in English) and the subject of the sentence is an implied you (be it singular or plural). So, as others have said, the 'us' is the object, so it's the accusative 'us' rather than the nominative 'we'.

"Let we go" or "let we us go" = Early Modern English (the subject is "we")

Cf. Late Modern English's "let us go", in which the subject is "you" which is not written because it is already understood.

"Let's go" = Late Modern English (the subject is "we")

Cf. other West Germanic languages: Laat we (ons) gaan (Dutch); Lassen wir uns gehen (German)