I think, perhaps, you are making this question seem harder than it actually is. Some of Martin Eden’s simple statuses in life lead to his being an outcast or an outsider.
For example, Martin Eden was an fatherless (or illegitimate) child of a traveling psychic. Both of these specifics lead to Eden being an automatic outcast. At that time, any illegitimate child (due to no fault of his or her own) was outcast by society. Further, having a parent who was a palm reader or fortune teller or psychic again puts the child at risk of being ostracized.
Further, both Jack London and Martin Eden grow up in the lower class. Again, this fact is an immediate factor in the character being outcast. Being in the lower class and experiencing extreme poverty in Oakland, California is going to ostracize both character and author from upper class life.
Finally, Martin Eden spends some time being a “hobo,” in that he is jobless and wandering in looking for adventure. During this time, he also becomes a prisoner due to his derelict behavior. This absolutely adds to Martin Eden’s outcast qualities. Being an outcast is almost in the definition of hobo in that a hobo is literally often cast out of homes where he begs for food.
Also consider that the self portrait of Martin Eden is also considered the self portrait of Jack London (the author). Even the first edition of the book contained an imagined image of Martin Eden with Jack London’s face. Just like Martin Eden, Jack London always found more adventure in life than in his education and writing.