How to find currency pairs that have biggest volatility and movements?
Create an EA or Indicator.
What algorithms would you use?
No need to create Volatility Indicators - The most common are already built-in - StdDev (Standard Deviation) and ATR (Average True Range).
Learn to use them (either independently or together) as they each have their own advantages and disadvantages.
There are other less common measures of volatility, but these two will do just fine for Forex symbols.