If you do weave one-liners into a story, you have to have an overall story as well, otherwise it doesn't really count as narrative.

Conjunctivitis.com — that’s a site for sore eyes.

This policeman came up to me with a pencil and a piece of very thin paper. He said, "I want you to trace someone for me."

So I rang up my local swimming baths. I said 'Is that the local swimming baths?' He said 'It depends where you're calling from.'

If you do weave one-liners into a story, you have to have an overall story as well, otherwise it doesn't really count as narrative.

I was in this restaurant and I asked for something herby. They gave me a Volkswagen with no driver.

If you compulsively pun you are called a paronomasiac.