Some, but by no means all, of the Oddfellows are heroes. However, though you do have Tarzan, Mary Poppins, and Randolph Carter as Oddfellows, you also have the necromancer Doctor Frankenstein and the undead Charles Babbage. They have a decidedly mixed reputation, though the English Crown did take the somewhat risky step of officially endorsing the group a few years ago.
‘Oddfellows” was originally a term for isolated tradesmen who did not have enough numbers for a proper guild. These days, however, it is more likely to refer to Imaginaries and Dreamers who, left on the outskirts of civilization due to their strange origins, have banded together for support. Oddfellows agitate for rights and also serve as guardians for Ordinaries who now live in a far crueler universe than they understand.
It could be said that Oddfellows fight for the sake of good; at the very least they seek to avoid disaster and provide at least some protection to society. They also refrain from using their powers to overawe Ordinaries and take advantage of them. In many ways, though, this is pragmatic – they understand that they can’t defeat the Ordinaries on their own so instead they try to win them over by example. How long this will last, no one knows.