Do you have problem with English or Polish?
In Polish the word order is less important than in English, In this sentence you can switch evertyhing around (with slight changes of stress on different words) as long as there is no pronoun at the end. (and stressed "mi" is "mnie")
On is in nominative, it is a subject. Mi is Dative it is object.
In fact, since we are operating on personal pronouns, it would work exactly the same way in English. I mean, you are still supposed to maintain a typical word order, but its meaning should be possible to decode regardless of how you order "he", "helped a lot", and "me". It shouldn't be too difficult understanding even the literal translation of "He me helped a lot" (which should not be confused with "Him I helped a lot").