Similar in that they are often used to negate something, "not...", "don't...". BUT, the meanings are different. 별로 means "so so", "barely satisfactory", "not to the extent that I would desire". 전혀 is already explained.

"전혀" means completely or never, 나는 술을 전혀 마시지 않는다. "별로" means not bad but not good.. 나는 술을 별로 좋아하지 않는다. "아주"means very..나는 술을 아주 좋아한다.. "매우" also almost same meaning with "아주" .. 나는 술을 매우 좋아한다.. "너무"also you can use as same meaning with "아주" 매우".. 나는 술을 너무 좋아한다. thank you. thank

I think 전혀 and 하나도 are closer.