I am not sure which language you want the explanation.
Let's do it in English, if you need more explanation in Hungarian, let us know in the Asker Note.
A few definitions:
"have (got) sb by the short and curlies (ALSO have (got) sb by the short hairs) SLANG: to have someone in your power"
http://www.freesearch.co.uk/dictionary/have (got) sb by the ...

"short and curlies
Noun. Basically the term refers to pubic hairs, however it is used figuratively in having got someone by the short and curlies - having complete power over someone. Orig military use. [1930s]"
http://www.peevish.co.uk/slang/s.htm

"have someone by the short and curlies:
American expression meaning to have someone at a disadvantage."
http://www.sex-lexis.com/Sex-Dictionary/have someone by the ...

I think you got the picture. This slang is in perfect parallel with "get soneone by the balls" - and it refers to the same body area- if you know what I mean...

I don't think there is a "similarly figurative" equivalent in Hungarian, the general term is "markában tart". It is used to refer to someone having ultimate power over another person, which is what the balls and hairs slang means, too.