because whatever is on the other end of that overflow pipe is overflowing

An overflow pipe on a (toilet cistern?) will leak if the rubber disc in the ballcock slide valve needs to be replaced.

Yes, the gasket between the overflow pipe and the tub can go bad, or it can leak around where the pipe is attached to the drain.

Extend the overflow pipe underground to a point where it is above ground.

Depends on what type of overflow and what it services and whether it is constantly happening or intermittent.