따위 normally has two meanings It means etc/and the like/and so on after a list of something. ex) 사과나 오렌지 따위를 넣어 만든 주스 : Juice made of apple or orange thingy. But it is more often used as a bound noun which comes after or in front of object(s)/event(s)/anything to emphasize your negative idea about them. 따위 also can be used as a independent noun which means 'that way(offensive)'. ex) 나는 사랑 '따위' 믿지 않아. I don't trust Love thingy. 그 '따위' 말로 내가 화가 풀릴 것 같아? Do you think I will blow off steam by that kind of words? (this became much more offensive by adding 따위) 말을 왜 그 '따위'로 하니? Why the h**l do you say in that way? (따위 in here is used as 'way/method/kind'

이따위 것 필요없어! I don't need such a thing! 이따위 일은 두번 다시 하지 않겠어. I will never do such a thing again. 이따위 짜증나는 상황에 시간을 낭비하고 싶지 않아. I don't want to waste my time for this annoying situation.

I think both two answers are good, but Ahtti's is more correct. Mostly, if 따위 is used for listing something such as a, b, c '따위' in each sentence, the sentences still have the same meaning without any change. And in this context, 따위 is interchangeable with '등'. If you want to translate '따위', which is used for negative and patronizing someone, just add some offensive adjectives considering each context when translating it into English.