Wanted to play the 057 Apocalypse from the new set, and he has a few of these stop clicks

Summon our full might: STOP. Apocalypse can't be damaged by opposing effects, healed, or chosen for Mastermind. // At the beginning of your turn, generate an Daemon bystander within six squares. // At the end of your turn, deal Apocalypse 1 unavoidable damage.

what counts as an opposing effect? Does that mean you just cant attack him at all?

Attacks, Poison, Submission Hold, damage from opponent-owned maps that's not Unavoidable damage, opposing special objects like Gamma Bomb, opposing traits that might deal damage... Lots of stuff comes to mind.

For that round yes, you can't attack him unless you have some way of making him unable to use his power (like wotr047b Gamora or wotr030 Donald Blake).
Poison and Mystic won't work either. It would have to be the effect that is not caused by something the player opposing Apocalypse controls, so probably map special rules(but not the location bonus).

In short any effect caused by something considered to be a part of your opponent's force will be a opponent effect.

You can attack, you just can't damage. Incapacitate would work, for example, and various special powers have effects which trigger on a hit.

-J

I should have been more precise.