[bash] An "and" operator for an "if" statement in Bash

What you have should work, unless ${STATUS} is empty. It would probably be better to do:

if ! [ "${STATUS}" -eq 200 ] 2> /dev/null && [ "${STRING}" != "${VALUE}" ]; then

or

if [ "${STATUS}" != 200 ] && [ "${STRING}" != "${VALUE}" ]; then

It's hard to say, since you haven't shown us exactly what is going wrong with your script.

Personal opinion: never use [[. It suppresses important error messages and is not portable to different shells.