what diff is in your car? if its the stock plastic, or even the non adjustable aluminum diff you wont have much success filling it with oil. nothing is sealed in this diff, it will just leak everything out in a short time. been there done that, ive even tried to seal the outputs and housing, just doesn't work. your best bet is to fill it with grease to keep it lubricated. an open diff is best for parking lots and roads.
in cars like these if you want to limit diff action you need an adjustable diff or some variety (fg makes an adjustable, adjustable 2 and 4 clutch, viscous, and powerlock style diffs)