Screwdriver

I couldn't figure out the etymology of screwdriver - as in the mixed drink. But the online etymology dictionary has this surmise:

Screwed/screwy had a sense of "drunk" since 19c.

I don't recall hearing that usage, but it's close to a lot of other slang for being drunk. By the way, there is no end of slang about alcohol and drunkenness, and I speculate that's because there has been an ongoing need to speak about it evasively.

When open discussion makes people nervous,
slang is often pressed into service.