This seems to me to be a pretty good example of the futility of trying to reduce meaning to definitions. You might paraphrase the verb as "having the right to dispose of property", but then an infinite regress of questions may follow. In this sense, defining "own" is as easy as defining "dog" – not at all easy.
Given your final version "Only I can say who can do something to X", I need to point out a few problems. First, anybody can say, utter or pronounce something: you presumably are using "can say" to refer to the concept of "right". Second, we would judge a definition to be wrong if it fails to include cases that would be recognized as being an instance of the concept. When two people co-own ("joint tenants") a thing, each has the right to dispose of the thing (legal details omitted): so it is wrong to make exclusivity part of the definition of owning.
Objections might be raised to using the word "dispose", which in common usage means "get rid of" (I've borrowed this from a more specialized philosophical context). I mean "do whatever you want". That might suggest that, if I own a brick, then by my definition I can rightfully bash you on the head with the brick, which is clearly false. The reason, though, has to do with the concept of "right", not the concept of "owning" (I also cannot bash you with a borrowed or rented brick).
If you're a speaker of English, I bet you do know what the word means, the problem is that you probably haven't thought about every allied concept and proposition that relates to owning.