I must preface this by saying that I am from England (i.e. not from America), so my comments refer to usage in England.
3: 'End up' means an 'end' that happens to a person or thing. It refers to a situation in which a person or thing find themselves after a series of other events. Examples are: 'she ended up getting arrested'; 'they ended up pretty drunk'; 'she ended up Prime Minister'; 'did you end up learning Zulu?'. It is equivalent French's 'il/elle a fini par...' Your example ('they end this paper up with a conclusion') sounds very foreign.
2: 'Wrap up means 'put an end to something': so your example is good English. Other examples: 'I am going to wrap this meeting up now' (i.e. end it); 'she said she would wrap up ten minutes ago!'; 'wrap up now, please, we have homes to go to'; 'before I wrap up, I want to say 'thanks' to Jane'; 'it is stylish to wrap up an article with a Kung Fu-tse quotation'.
1: 'Wind up' is interchangeable with 'end up', so again your example sounds very foreign. 'Wind up' means an 'end' that happens to somebody, not an 'end' that they bring about on purpose. For example: (this is a very common phrase and not just my morbidity) 'he wound up dead'. 'Wound' is the past tense of 'wind'. Or 'I was so bored that I wound up just going home'.
Note that these phrases have other uses that are not linked to 'ending'. For example 'wind up' also means to 'annoy somebody'. For example: 'he really wound her up today, I think that she might fire him', meaning: 'he really annoyed her'.
So you will see that only one of your examples is good English, namely: 'they wrap this paper up with a conclusion'. I hope that the distinction between the two types of 'end' is clear. One (wrap up) is an 'end' that you bring about by a purposeful act of ending. The other two (wind up and end up) refer to the state in which people or things are left at the end of a series of events. I hope that you haven't ended up confused.