If the OC is showing a $0 balance then it is highly likely they have sold the account.
Once they sell the account, they can not collect payment on it. You must deal with whoever owns the account.
If the OC is showing a balance, there is a good chance they still own the account. You want to call and speak with them regarding the account and find out of they own the account and if they will accept payment.
It is up to the OC, sometimes they will accept payment, other times they make you deal with the CA.
Closed accounts with balances being reported as a TL are included in your util.
When you pay that account to $0, it is not being included. This could change your util drastically and it could not. Not only is the balance removed from util, the CL Is as well.
Let's say you have a an old CO showing a balance of $1000 and a CL of $1000 and a current CC with a CL of $200, balance of $200.
Your util right now is $1200/$1200 = 100%
You pay/settle the old CO so that it has a $0 balance, your new util would be $200/$200 = 100%
Now, I realize that it will likely never be exactly 100%, but you get my point.
If it changes your util greatly, then chances are you'll gain some points. If it doesn't change your util or changes your util little, the less score gain you will get.
Once an account is CO, having it show settled is not going to hurt it worse. FICO reads the worse derogatory for each account and dings you for that......so with a CO account, FICO will ding you for a CO.