Should I pay off old collection accounts ? Will it improve my credit score?

You'd be surprised. It's always good to pay off debt that you legally owe, if you can afford it. However, be aware of a couple things:
1. If the Statute Of Limitations has expired on the debt, and you make a payment that's not paying it off in full, that re-starts the SOL clock and the company can and very well may sue you for the rest of the debt.
2. Paying off old collections is great for peace of mind and a sense of doing the right thing. However, it does very little for your credit. A lot of companies will not agree (in writing) to completely remove the listing from your credit report. It will change to show a zero balance, but it will still show that it went to collections, and how long it was in collections. It will still drop off (age out) after 7 years from the date it went into default, though.