I understand that these three expressions are an invitation to do something or go somewhere. I would use “давай” as in “come on” or “come with me”. “поехали” and ”пойдём” would be more like “let’s go”, but I think it’s a bit too simplistic.
In which case either of these expressions would be preferred over the other, and why?
What words must we use with each expression (e.g. must be followed by a verb or must be followed by a location)?