These 3 words happens in different scenes. 没关系:(formal or not very informal). when someone do a wrong thing, but it is not influence to you, when he say sorry to you :“对不起", the only answer is "没关系"！ Of course, if it is a major accident, such as car accident, you get injured, when the driver say sorry to you, you don't need say anything. 不要紧：(not very formal and informal). means don't worry about me. (when someone concerned about you) You get fever in your company, someone worry aout you,"How about you?""Are you OK?" you should say "我不要紧", means I'm OK. or Not very bad, I can continue working. A borrowed a book from B, and promise to give back in 3 days. but the date delay. after 5 days, A say"I'm so sorry." you shold say:"不要紧" means never mind. sililar to "没关系" 无所谓：(formal and informal) means "I don't mind something". A,B,C, three people in a room. A says to B"C is smoking now", B replys"无所谓"means B don't mind. There are 10 people in my familly. I'm host. I give each one an apple. You get the smallest apple. At this time, if one people say"your apple is the smallest!". you don't want to embrassed the host, so you say无所谓，都一样.means I don't mind bigger or smaller. But, at this time, If I say "Sorry to give you the smallest one", you should say"不要紧,小的说不定更甜呢。"means you don't mind it is the smallest one. For not embarrased the host, you can say"the smallest one is the sweetest one."

“没关系”means: It's ok. We use it when people say 'Sorry' to us. “不要紧”is similar with "没关系" “无所谓”means: That's not important / I don't care / Everything's ok. It's a little like "随便"（whatever）

没关系和不要紧意思差不多 无所谓 1.说不上，比如，我只是说说体会，无所谓报告。2.不在乎，比如，对于去不去吃饭，我无所谓。

我个人的见解，没关系是礼貌用语，比如别人不小心碰撞到你，对你说对不起，你可以回答没关系；但是无所谓却带有一定的贬义，比如你对某人很失望了，于是对这个人的好坏也无所谓了。

没关系 That's ok. 不要紧 No worries. 无所谓 Never mind or I don't care. 没关系 A:Sorry that I didn't finish my homework. B:没关系(That's ok.) 不要紧 A:Are you ok? B:不要紧(I'm good) 无所谓 A: I don't love you anymore! B: 无所谓(find, I don't even care!)