The freshwater eels that live along the east coast of Australia breed in the coral sea. The adults go through a number of changes as they make their way to the ocean, going from a muddy green/brown colour to silvery on the sides. Their eyes get larger, too.
Once they make it to the ocean, they swim north/north-east to the coral sea, dive deep, mate and die. They don't return. The eggs hatch into larvae which change in appearance as they develop and swim for the coast. In one of the stages, called leptocephalus, they are flat and thin - shaped a bit like a wide gum leaf - and are transparent. By the time they reach the coast they are 'glass eels', at which point they're starting to develop the eel-like shape of the adults but are still transparent. Then they become elvers, which are a miniature version of the adult but extremely tiny. A couple of years ago I caught one as it swam up a creek and it was about the thickness of a pencil lead and only 4-5cm long.
For all of those wondering how small eels could have made it into ponds or backyard pools if they weren't bred there, the answer is simple. The urge for elvers to head inland is strong. They'll go up waterways as far as they can go, but will also crawl over land to find isolated bodies of water, especially on rainy, or even just humid, nights. They're tiny, so often go unnoticed. Even larger eels will move across land if they must. Keep in mind, too, that we're all looking at the assorted ponds and dams as they appear now. Try to imagine the same bodies of water in a wet year, when the dams may have flooded over or even just when the rain has come down so hard a thin sheet of water is running across the ground, because that's probably when the eels moved in there. On a similar vein, I've seen green tree frogs in water tanks and outdoor dunnies in areas of almost desert-like dryness. It seems odd until one thinks about how many years they've probably been there and how many freakish wet years may have occurred in that time.
Once eels have settled in to a freshwater pond or dam, there's no schedule or time-line for when they must go back to the ocean to breed so they can stay there for many years. It's not unheard of for eels to live in the same pond or dam for 25 years or more. That explains all of the eels living in land-locked dams and ponds for many years. Like the elvers, even big eels can move across land on a wet night. I once saw a huge (at least 1.5m) long-finned eel on the side of the Pacific Highway in Sydney - it got hit by a car while moving across land.