The sorcery doll is taken from the idea of grave goods. Basically, you are asking the King of Hell to harm your enemies - or take your enemy to his realm. Those that use them do not have happy endings - > all magic has a price.
as for Voodoo doll - that is a 20th century association due to movies, media, and the Christian right trying to make Voodoo connected with Satanism.
A lot of 'magic' seems archetypal and cross cultural . Poppet, corn dolly , fif faf , Paktol (Philippines ) , Netc . nearly all cultures have some version of this. Generally it comes under 'sympathetic magic'.
Yeah, effigies are part of many folk religions. In southern China there were (and maybe still are) "maple men" (fengren) and other kinds of wooden figures used like Voodoo dolls. Sometimes they were just natural growths on trees that were human-shaped, other times they were carved figurines. There are probably dozens of variations of this kind of magical effigy just in China alone.