Reply to "He told some stories of personal experience..."

He told some stories of personal experience so well that he made a lot of people cry a little.

In constructions with 'so...(adjective or adverb)...that,' 'so' and 'that' go together.

'So' is an adverb modifying, in your sentence, Volcano, the adverb 'well.'

Then, 'that' is the conjunction that introduces the clause to complete the meaning of 'so well.'

Here's an entry in the LDOCE for 'so' as an adverb:

so ... (that)

He was so weak that he could hardly stand up.

There was so much smoke that they couldn't see across the hallway.

Everything happened so quickly I hadn't time to think.

Here's an entry from the LDOCE at 'that' as a conjunction:

used after a phrase with 'so' or 'such' to introduce a clause that shows the result of something:

I was so tired that I fell asleep.

The school was so badly damaged that it had to be pulled down.

We had been away for such a long time that I had forgotten her name.