I have 16 collections listed on my credit report stemming from my divorce a couple years ago, and my credit is truly horrendous.?

It won't be a stellar increase. It might go to 600 and the individual account will be noted as paid. Understand that once a valid collection is on your profile, it stays there. The collection agency cannot force the credit bureaus to remove truthful, accurate data from your profile. The collection agencies will tell you anything to get the money. If all the negative information could be removed, then the credit report would be useless as everyone would have FICOs of 850.

Unless you plan to buy a house, finance a car, or apply for credit or a loan, you can just ignore them and let them fall off after a 7 year period. Paying off your debts will not increase your credit score; there isn't a difference between a collection that has been paid off or still has balance. You can try to pay the debt collectors to remove the derogatory accounts.

jk