Captain Oicunn’s text reads:

After executing a maneuver, each enemy ship you are touching suffers 1 damage.

Grammatically, the clause after executing a maneuver applies to the subject of this sentence, each enemy ship. This would mean that when an enemy overlaps Oicunn, the enemy suffers 1 damage. However, my impression of Oicunn is that he deals this damage to enemy ships when he overlaps them. Which is correct? Am I misunderstanding the card, or is it just very poorly worded?

Thanks!

Overlapping is a fancy word for bumping at the end of the maneuver. So usually you'll only bump one ship on YOUR maneuver. Their maneuver doesn't matter.

They can bump Oicunn and not take damage all day long.

You can use the Dauntless title and Daredevil EPT to cause another point of damage as well.

They can bump Oicunn and not take damage all day long.

Unless Oicunn equips Anti-pursuit lasers

But yes, Oicunn only causes damage to ships he is still "touching" at the END of his maneuver. Generally this is just one ship even if he has "backed over" multiple ships because overlaps force him back into another overlap situation which forces him back even further. Now I guess the way the rules are currently if you happened to be blocked back all the way to your starting position then any ships that were "touching" you are still touching you and would take the damage.

I believe that the bit you are looking for is the definition of the word "you" in X-Wing.

Rules Reference Guide, page 8:

The word “you” on a Ship card refers to the corresponding ship. Abilities on Ship cards cannot affect other ships unless the ability specifies otherwise.