For example, instead of "barking up the wrong tree", someone uses "pulling out the wrong plant". Consciously or not, is there a term for saying idioms in your own words?
Such off-center words and phrases are called malapropisms, and the speaker is called a malapropist.
mal·a·prop·ism noun \ˈma-lə-ˌprä-ˌpi-zəm\ : an amusing error that occurs when a person mistakenly uses a word that sounds like another word but that has a very different meaning
These can be called Ziva-isms, named after the character Ziva David from NCIS. Here's a long list of some of hers.