Is the oath valid that the employer did not say, "You will work without pay as long as there is no work," even if he might have meant it or the questioner understood it that way? And does this entail expiation if the oath is invalid?

Faith is built upon intention. So, if you intended, by your oath, to deny the employer's statement of the aforementioned sentence, then there is no harm upon you in this—God willing—as long as the wording of your oath allows for it, since a condition for a word to be interpreted according to one's intention is that it must be capable of bearing that meaning.