"From then on" or "since then"?

The two of them generally mean the same thing, and can quite correctly be used interchangeably. So:

Since then, the two children lived alone...

Means the exact same as:

From then on, the two children lived alone...

But, there is a very slight difference here. Since then can mean that the action happened at some point in time after the event. I.E, at some point after their parents died, they started living alone. From then on does not give that kind of meaning that from the very moment, they lived alone.

However, there is a possibility, that in certain situations, from then on can be taken to mean from that moment until another, when used along with other words. For example:

From then on until the day they (did something), the two children live alone...

This sentence style isn't often used when using since then, because since then is often understood as from one moment until the present. However this is ambiguous, since one can still use the word until to give the same sense.

Since then, until the day they (did something), the two children live alone...

In conclusion, if you meant that they lived alone from the very moment their parents died, from then on is slightly more correct.

I'm afraid I'm going to have to disagree with LightMikE.

The difference between "since then" and "from then on" is one of grammatical aspect.

"Since then" is spoken about things that are still going on. So it would be correct to write

Since then, the two children have lived alone [implying and today they still do].

But the sentence you have, since it's about something that happened in the past but is no longer relevant, requires "from then on."

Similarly, "From then on" is spoken about things that are no longer going on. So it's correct to write

From then on, the two children lived alone [implying but today they don't].

but it would be incorrect to write

From then on, the two children have lived alone.

Since I don't know whether the two children no longer live alone because they live with other people or because they're dead, it might be clearer to show first-person examples. So these would be correct:

When I was a kid, I ate some disgusting French fries. Since then I've hated French fries, which is why I don't ever order them at restaurants.

When I was a kid, I ate some disgusting French fries. From then on I hated French fries, until my mother made me try some a few years later, and now I love them again.

But to switch "since then" and "from then on" in the above sentences would make them incorrect.