I would try plastic taping knives such as these
If these are not sharp enough, I would move on to credit cards. Yes, credit cards (use the ones you got in the mail that you do not want). They are softer than metal, but have a fairly sharp edge.
If there is still stubborn residue, I would use a dull metal taping knife (or putty knife).
If there is remaining stickiness or oiliness, I would use a grease cutting cleaner like Fantastik. If that was in sufficient, I would move on to alcohol. Then mineral spirits.
Only if all these failed would I move on to sharp scrapers or sanding.
Yes, it is slow and tedious. But I have cleaned up a floor that looked just like that in a few hours and it came out beautifully (even if I was cranky, exhausted and far from beautiful).