So spellcasters can use counter casting against spells but not critter/spirit powers. Can the edge magic resistance counter critter/spirit powers?

Well I'm not too sure about SR3 and lower, but in SR4 a magicians counterspelling is not effective against critter spells (except innate spell and maybe one other) and spirit powers. From the reading of the magic resistance quality it seems that it adds 1 dice per rating to Spell Resistance Tests (and cites the page for normal spells) leads me to believe this has no effect on critter powers. Arcane Arrester also does nothing against critter powers. The spell resistance adept power explicitly states that it does not work on critter powers, which maybe you can take as further evidence that the magic resistance quality does not work on critter powers.

Can anyone come up with something that does help against critter powers?

Right, you mean Critter *powers*, because if they're actually using spells, those are spells.

I agree: effects that work as Spell Resistance are not 'Magic Resistance'.

A high Body/Willpower combined with a LMG?

Thanks, lol.

There are some adept powers like Iron Will and Piercing Senses that work on specific categories of critter powers.

There had also been the discussion, that Banishing can be used as some sort of "counterspelling" against spirit/critter-powers. IMHO magic is magic, i see no difference if somebody has the innate "power" to manipulate magic to breathe fire, or if somebody "learned" to manipulate magic the same way. In my games i added the mentioned alternate rule that banishing works.