You want to execute usage
in case either 1st or 2nd condition are accomplished. For that, you can do:
[ -z $a ] || [ -z $b ] && usage
Test:
$ [ -z "$a" ] || [ -z "$b" ] && echo "yes"
yes
$ b="a"
$ [ -z "$a" ] || [ -z "$b" ] && echo "yes"
yes
$ a="a"
$ [ -z "$a" ] || [ -z "$b" ] && echo "yes"
$