"Your Go" is the one that bothers me. The client makes it pretty clear when it's your turn, and you're on a fairly short timer to boot. IMO, the only reason to send "Your Go" is to be obnoxious, and I immediately mute anyone who does it.
"Nice" gets a pass from me. Half the time it means "you're only winning because you got lucky," but the other half it genuinely seems to mean "cool combo" or "nice pull".
The problem with the cartoon emotes is that I have no idea whether my opponent thinks they mean the same thing as I do. And yeah, I don't know how people get access to them, but I don't have any.