Baby oil is scented mineral oil, which when ingested, clogs in the intestines. Since your cat is sure to lick her coat, I would recommend that you definitely not use baby oil on her. It is also going to rub all over your furniture and floor, and attract more dust to her, not clean her.
My recommendation is that you either take the cat to a professional groomer who will brush out, and cut out the mattes safely, or shave the cat if that's what's needed. Second option is that you do this yourself, but I would recommend that you only do the brushing part, as the cutting/shaving should be left to professionals.
After your cat is back from the groomers, or once you are done with her, make sure you groom her every day, or every other day, and make sure this does not happen again. Also, a cat that has lost interest in grooming itself is possibly ill. Watch out for any other signs.
My recommendation is that you either take the cat to a professional groomer who will brush out, and cut out the mattes safely, or shave the cat if that's what's needed. Second option is that you do this yourself, but I would recommend that you only do the brushing part, as the cutting/shaving should be left to professionals.
After your cat is back from the groomers, or once you are done with her, make sure you groom her every day, or every other day, and make sure this does not happen again. Also, a cat that has lost interest in grooming itself is possibly ill. Watch out for any other signs.