What is the most effective way to get our order filled when there is same open interest and same traded quantity?

What matters to get your order executed is the market depth at the point you are placing your order. Market depth is basically the screen that shows quantity and best available rates. If you are trading things like Nifty, you don’t have to be worried at all.

As a retail you have only two options, either limit order or market order. I have seen a lot of people trying to catch the best price, placing a limit order and then that price never comes. So personally I have always used market orders to enter and exit positions. Check this: http://zerodha.com/z-connect/zerodha-60-day-challenge/winners/nithin-zero-to-zerodha

Most effective way is a market order if it is nifty or banknifty.
Traded qty or open interest hasnothing to do with your order filling.