One of the few things I remember from high school health class is the origins of the slang term for gonorrhea...

"Clapier" is an old-timey French word for whorehouse. That one seems obvious.

The following is really gross...

But in addition to that, "the clap" was also a doctors preferred form of treatment for expelling the discharge from his patient's private parts. He would get an assistant to hold the penis up as if it were erect and "clap" his hands together, causing the goo to exit the body.

As for any other slang terms for STDs, I can't really help you.