I remember learning the rule for when to use cualquier, cualquiera, and cualesquiera, but was always confused about the exact differences. When should each be used, and what role do number, gender, and word placement play? Specifically, what should the translation be in the phrase "any of us," and why is that the proper choice?
"Cualquiera" can work as an determinative adjective (used with a noun) or as a pronoun.
In this site it is explained its use as a determinative:
It is the singular form and it appears before the noun, which can be both masculine and feminine:
Coge cualquier libro
Lee cualquier página
It is the singular form and it appears after the noun, which can be both masculine and feminine:
Coge un libro cualquiera
Lee una página cualquiera
So, use cualquier or cualquiera when you want to say "any", one single thing. "Cualquier" is the shorted form, and "cualquiera" is the full form. Just pick any of them and be careful with the placement.
It is the plural form and it appears after the noun, which can be both masculine and feminine:
Coge dos libros cualesquiera
Lee dos páginas cualesquiera
However, it is quite spread the use of "cualquiera" in plural nouns, but this is not correct:
Coge dos libros cualquiera*
About its use as pronoun, [in this site] we read:
In its pronominal function, it's always "cualquiera".
Esto lo sabe cualquiera.
It can also take a complement preceded by "de".
Cualquiera de estas llaves abre la puerta.
So, having said that, let's translate "any of us". "Of us" translates as "de nosotros", that is, a complement preceded by "de". So, it must be "cualquiera", as it is in the pronominal form:
Cualquiera de nosotros.