to drain something of its force, meaning, or validity; to nullify or make void
The verb κενόω literally means "to make empty," and in ordinary Greek it drained containers, depopulated cities, and emptied armies onto a plain. It is built on the adjective κενός, "empty." Paul, though, never uses it of a physical thing. In every one of these four verses the object is an idea or a claim, and the verb strips it of its force or its truth.
In Romans 4:14 faith itself is "emptied" and the promise "made void" if the inheritance depends on keeping the law; here the word stands right beside καταργέω, the plainer term for cancelling something so it no longer works. In First Corinthians 1:17 Paul refuses polished rhetoric so that the cross is not "emptied" of its saving power. And twice he speaks of a boast being emptied: no one will drain his ground for pride of its substance (First Corinthians 9:15), and he sends helpers ahead so that his boast about the Corinthians will not "prove hollow" (Second Corinthians 9:3).
The common thread is a reality that looks solid being shown to have nothing behind it, or being robbed of whatever made it effective. The opposite move would be to fill something up, not to empty it.