On the previous week news (14-Aug-2018) we found one dam overflows because of excess water. Few days it stayed like that way. Is it affect it's strength

Possibly but I wouldn't stand there watching to see if it holds... RUN! Typically when dams are built, a spillway(s) is also built to keep the water level behind the dam at a safe level.

Did I mention RUN... for much higher ground... and safe distance.

Depends on the dam construction. Earthen dams are usually the ones to fail. Concrete dams rarely. All dams should have a spillway. My friend has a 5 acre pond with an earthen dam. It has a stone bed spillway AND another 8" PVC pipe emergency overflow pipe.

A concrete dam may indeed fail if over-topped for too long - it all depends on how it's designed. Water flowing over the top may not harm the concrete itself, but can cause scouring at the base and along the embankments on either side.