Please note that this answer assumes that steel wind strike does not naturally grant advantage on all its attacks (even without invisibility). I believe this is the intended interpretation, but it may not be the RAW reading -- see this question.
Either the first one, or none of them.
Take eldritch blast as precedent, as the wording is similar. Eldritch blast calls for ranged spell attacks against multiple targets, specifically making "a separate attack roll for each beam" (PHB p.237), similar enough to steel wind strike's "make a melee spell attack against each target."
The Sage Advice Compendium reads as follows, in response to a question asking whether the beams from eldritch blast are simultaneous:
Even though the duration of each of these spells is instantaneous, you choose the targets and resolve the attacks consecutively, not all at once. If you want, you can declare all your targets before making any attacks, but you would still roll separately for each attack (and damage, if appropriate).
Thus, since each attack happens in series, and invisibility ends either when you attack or cast a spell, there are two distinct points when the invisibility could end. If "casting a spell" is considered to occur when you begin casting a spell, then you become visible before any attacks are made. Otherwise, it will last until the first attack breaks invisibility, and that one attack will be made with advantage.
So the issue rests on when the character is considered to have cast a spell. I'm not aware of an official ruling that would make this determination, but if one exists, it will be the determining factor.