Here's the deal... anytime you pay ANYTHING on an account, it resets the 7 year clock for being included on your report. It's 7 years from the date of LAST ACTIVITY.
So... I don't know where the 2 year "limit" comes into play... but I do know this. Don't pay a DIME on those collection accounts unless you get an agreement in writing from them that they will delete the account from all reporting agencies and not report it again. Otherwise, you will pay these collection accounts off, and be stuck with accounts that show "Was Late, Paid In Collection, Closed by Credit Grantor", and these accounts will be there for SEVEN MORE YEARS.
Keep any OPEN accounts open, bring them current, and pay at least the minimum ON TIME, EVERY TIME. If you do this and only this, and just wait 5 more years, your collection accounts will fall off, and you will have 5 years of good payment history. That alone will raise your scores significantly.
You can try to challenge the validity of the collection accounts, but that probably won't work very well, and the reporting agencies will most likely start calling your challenges "frivolous" after the first 2 or 3 (unless you can prove identity theft, fraud, or negligence on the part of the creditors).
Your best bet is to pay the OPEN accounts on time, and get deletion letters for the collection accounts. If that is successful, you can raise your scores significantly over the next 24 months.