The two general strategies often recommended for reducing debt are to pay off the smallest debts first, so that you feel a sense of progress by closing accounts, or pay off the highest interest debts first, because that saves you a little more money in the long run.
You certainly can try to contact your lenders and negotiate a reduction in the amount of debt. If you pay off your debts for less than you owed, that fact will be noted on your credit report and may reduce your score. But it will also show that you are paid off which is beneficial. The lender is more likely to accept a compromise if you were able to pay a lump sum immediately. For example, if you owed one lender $5000 and were planning to pay it off $100 a month for seven years including interest, there would be very little incentive for the lender agree to a reduction if you were simply going to pay off $50 a month for seven years. But if you offered to pay $3000 in a lump sum to close the account now, they might be more receptive.
There are some consumer debt counseling services that have more experience negotiating with lenders and which may be able to help you. However, some consumer debt counseling services are scams. I can’t really advise you on the best way to pick a good service, just be very careful and try to find a service that will work with you for free instead of taking a cut for themselves off the top. That could end up putting you in a worse position. And any company that promises to “clean” your credit report or “fix” your credit report without you paying off your debts is almost certainly a scam.