If an owl tries to fly up on top of a tree and gets caught underneath a block (like tree leaves), it continually takes damage and eventually dies.

Can confirm. Its really sad, because I made a very nice home for them, but they just off themselves :(
Its not just trees. Its any ceiling.

Same here. As a temporary workaround I added this to EntityOwl:

@Override
public boolean attackEntityFrom(DamageSource source, float amount)
{
  if(source == DamageSource.IN_WALL)
    return false;
    
  return super.attackEntityFrom(source, amount);
}

I tried filtering it to just Blocks.LEAVES but it didn't jive with the tree mod I use, or I did it wrong.

I can also confirm this behavior happening. It would be nice if the mod author would update this workaround supplied by Naqaden. Seems like an Owl being immune to suffocate damage would not be an issue...

Tracked down the true cause, submitted a fix to the new repo for enderzoo: SleepyTrousers/EnderIO-1.5-1.12#5036