In this context, "I avoid consuming sugar" is correct. Although, "I don't eat sugar" is probably more common. As for "keep away"... Something is "kept away" if you are avoiding it. You could say: "I keep away from that stuff!", or "I keep away from sugar". Although, this maybe has more to do with physical distance than the act of consuming sugar. I hope this helps!

Well, “I keep away consuming sugar” is wrong. Usually, people say “I stay away from sugar” ~ şekerden uzak duruyorum gibi bir şey “I avoid consuming sugar” is the same thing as “ I stay away from sugar” it is just another way of saying the same thing. “Avoid” in a sentence: I avoid crowded places I avoid fights I avoid eye contact

We don't use the term. "Keep away," in the US. We may say, "please keep the sugar away from me because I'm trying to avoid using it. Sugar is making me fat."