They are all different pronouns used in different situations. (Please bear in mind that I am not a Russian native speaker but I think I can answer this question) Моё, is a personal possessive pronoun used with neuter nouns in the nominative case. Мне, is a personal pronoun (sometimes translated as "to me") which is used with the dative and instrumental cases. Я is most often translated as "I" and is used with the nominative case. Basically if you haven't already discovered this; the pronouns in Russian are pretty extensive.

Моё - is my, мне - for me, я - I'm

Моё=my Мне=to me Я=I