Right.it is very indecent expression means ... the same as the English word beginning with "f".
I am not sure what you mean by "connotation", but ё-моё is not obscene or indecent word, like the English f-words. It is just colloquial, as well as all those you mentioned (with just a minor correction: японский городовой).You may have noticed that a bunch of Russian expressions (completely meaningless, if not understand the subtext) - begins with the letter Ё - for example, "ёшкин кот", "ёперный театр", ёпонской городовой", "ёлки-моталки" - yes, all they express surprise, admiration or, on the contrary, the disappointment, but the meaning (connotation) is the same - to the English letter F))
Unfortunately, not. Моё is added to make a rhyme out of ё and in order to exclude possible offense of others.So, just to be clear, ё моё means something like, "eff me!", as a euphemism for "fuck me!"...? And ёб твою мать means something like "motherfucker!"...?
I'm pretty sure lots of Russian of Russians would disagree, from @yakor above to everyone I know. Ё моё can at the very least also suggest annoyance (which is not the same as disappointment), exasperation and vexation in the situations I have heard it uttered.As already said, the Russian interjection expresses only suprise or disappointemnt and nothing more.
Give us an example, please. A mere description of how the expression can be used isn’t of any help unless there’s a good bunch of example sentences.