Let's say that Oicunn overlaps a ship. When backing up in the manuever, he would overlap another ship, and thus has to keep backing up (eg he moved through 2 ships).

Does his ability trigger on each ship that he pulls back through? That is, he moves through Defender1 and finishes his movement overlapping Defender2. In backup up his ship along his movement template, he has to back up to his starting position because he would then overlap Defender1 as well. Dooes his ability trigger on both of those ships?

No. He actually doesn't move back. You mive the model backwards to find the position where it ends up. He never actually hitvthe other ship.

And ao he deals damage to whatever ships he ends up touching.

His ability states "after executing a maneuver" which means only the final position matters. Whatever happens during the move is irrelevant. It only triggers after your move is done, and damages any enemy ship you are still touching.