If your legs are sore during and after you ride your bike and you pedal strenuously going up hills, then your problem isn't cleats or lack of cleats. It's likely that you just pedal in too hard a gear. Shift to a lower gear if you have one. If you don't have low enough gears, then you need to remedy that by either getting the stuff to give you lower gearing on that bike or buy a different bike that has the lower gearing.

IMO, you really only need cleats once you get to the point where you are developing a high cadence and your feet no longer can stay firmly on the pedals.