The old man died . . . . . . . . overeating.

The correct preposition is "of".

Explanation:

We commonly use the preposition "of" to indicate the cause of death.

Examples: He died of cancer. She died of a heart attack.

In the same way, "The old man died of overeating" correctly implies that overeating was the cause of his death.

Incorrect Options:

with – This implies being accompanied by something, not a cause.

from – Although sometimes used interchangeably, "of" is more idiomatic when referring to causes of death.

in – This indicates a location or situation, which doesn't fit here.