Yes, && (AND) is the correct operator if you want to check "if @nx is not equal to @n1, not equal to @n2, not equal to @n3".
if (@nx!=@n1 && @nx!=@n2 && @nx!=@n3) {
If you take the "not" part out and group the rest in parenthesis then you would use || (OR):
if ( !(@nx==@n1 || @nx==@n2 || @nx==@n3) ) {
"if not (@nx equal to @n1, or @nx equal to @n2, or @nx equal to @n3)"