Very particularly, I'm looking at the Torkoal, Stunfisk and Drapion ones. If you look at the background, lighting, focus and other effects, the Pokémon appear just a little like a sticker slapped on a background at the moment. What I mean is that by adding some soft white brushing and soft back shading, you can accentuate a piece and make it look a lot more authentic; as if it has depth. This can also further be achieved by some good sharpening and blurring, and also through effects like c4ds (though those aren't usually used in avatars and small pieces). The resources thread has a lot on depth, and I would recommend you take a look there too, since that goes a lot more in-depth (haha, get it?) and I actually learnt a lot there.
I see what you mean, however that was kinda the look i was going for with these, kinda like some trading cards. I never intended for them to fully blend into the backgrounds, they were supposed to be highlighted by their almost 3-D sorta way they jump out from the backgrounds.
I will however take a look at the resources thread you mentioned as i'm always open to learning new things :D