And, honestly, a lot of the characters in the RP should strictly-speaking lose some or all of their powers when not in their home universe, not least because the laws of physics are not compatible between different universes. We are ignoring that because it would make for a bad RP if we didn't.
There's a rule from a pretty good fanfic that I'm using, which states: Even when switching universes, you maintain the properties of your own universe rather than that of the universe you're visiting.
So if you're a Loony Tunes character, getting hit by Berserker will still flatten you, but you'll be able to walk it off because toon physics. At the same time, if you come from a universe where it's proven that people have no souls and are just a collection of electrical impulses, no one will be able to soul-fuck you because you don't have one.
And I'm not ignoring anything. Luka, for example, still has the spirits from his universe, but they've lost their connection with their world, and thus are weakened, even if he hasn't had a chance to find that out IC.