As Cambridge Advanced Learner's Dictionary says, in the UK the idiomatic standard for distinguishing the humorous and strange senses is...
funny ha-ha, or funny peculiar?
OED's first citation for funny = humorous is 1756, 50 years before funny = curious, strange. But it's worth noting that their first entry for fun is a few decades earlier in 1685 - for the verb form...
to fun - to cheat, hoax; also, to cajole.
That exact sense is now obsolete, but "I'm just funning you" = "I'm only joking" is still current, and the also-current usage fool somebody straddles both the cheat/trick and tease/make fun of senses. In which context it's also worth noting that OED trace the origin of fun to C14 fon = foolish, silly - a sense which still exists as fond (of a hope or belief) foolishly optimistic.
It's perfectly normal for the meaning of English words to shift over time, and for a single word to take on multiple senses which increasingly diverge. Sometimes, as with terrible/terrific or awful/awesome, we end up using different forms of the root word for the different senses. With other words (such as cry = call out/weep) only context indicates the intended meaning.
This is purely my own opinion, but I suspect words associated with feelings, value judgements, etc. are more likely to change or acquire additional meanings, because they relate to real-world referents that may actually differ between individuals (one person may cry tears of laughter on seeing a man slip on a banana skin; another may cry tears of sorrow as he thinks of the pain and possibly permanent injury that may result).