Yes, but with certain restrictions.
The only Wii game that allows trading is My Pokémon Ranch, and it does not allow trading between more than one game. Instead, an NPC trainer comes by with a different pokémon each day. Sometimes you can trade the pokémon you transferred over from your DS for these pokémon, and sometimes you cannot. When you can, those pokémon are considered yours and can be traded back the the DS that the original pokémon came from.
Pokémon Battle Revolution can import pokémon from a DS cart, however they do not leave the DS when you do, and once you do this you can only use pokémon from that cart unless you start the game over. You also cannot trade the pokémon from Pokémon Battle Revolution to another game. You can, however, earn items that can be transferred to the DS game, where you can use them to alter the original pokémon.