TTMIK says 싫어 is a passive lack of preference, while 미뭐 is an active hate, but can only be used for things with brains. 싫어해 can be used as a more active dislike.
I think the latter is stronger (hate), while the former is more like a simple "don't like". Not sure though.
Really? I always though it was the other way around... (I have little experience on the language, so it was just a feeling I had...)
I see I wrote that answer 5 months ago. Not sure I would still give such a binary answer. I think it depends on who is talking to you and associated context: if your wife or girlfriend were to say 미워 during a fight, the strength might depend on the severity of the fight.
Looking up the roots in translation, my impression was 싫다 means torn from liking something, 싫어하다 is to be torn from liking something -- the verb rather than adjective, 밉다 is starting to (repeatedly, intentionally) get on your nerves, 미워하다 the verb form get on your nerves (refusing to desist). The latter may be stronger in the verb sense, not so much in the adjective. Certainly don't take my word for it though -- touchy subject . . .
you would never say 미워 to a stranger, it's much more intimate. also it's more a subtle thing than 싫어. to me at any rate it's more like not liking something - so i find this exercise confusing.
There is also the option of "I dislike that man," but that is exactly what I typed, "I don't like that man." Got it wrong.