You use funnily enoughbefore describing something unusual. We don't really use funny enough. The only situation I can think of is if something meets a decent level of humour. You could say "the movie was funny enough". But it is pretty rare.

1. Which version is more common? I have never heard anyone say 'Funny enough' as a stand-alone phrase to show that a situation is unusual. It sounds wrong to me, while 'funnily enough' sounds normal. 2. Or is there any context that one is preferable over the other? Yes. * If you want to say that something is sufficiently amusing (as @PaulBacon says 'meeting a decent level of humour' ) you would say that it was 'funny enough'. For example, "Should I tell that joke about the elephants in my speech?" "No. It isn't funny enough". NB I presume this is the construction that @Dania is referring to. * To highlight the fact that you are telling someone about an unusual situation or surprising coincidence, the only phrase I am aware of is "Funnily enough" . In this context, 'funny' means 'strange'. We say "Funnily enough" in just the same way as we might say "Oddly enough" or "Strangely enough". I can see no grammatical logic at all in saying "Funny" in this situation. It has to be an adverb.

Wow. I didn't even know "funnily enough" could be such a word until I looked it up and found out it is actually in the dictionary. But the fact that a usage is acceptable doesn’t mean you have to use it. I would definitely prefer "funny enough."

Here is the grammar: Enough is one of those words that can be used as an adjective and an adverb Here it is an adverb, so it is used to modify an adjective in this case it goes after the adjective it modifies. As you notice ADJECTIVE so it is funny and not funnily.