I think the Fire Flowers can be used either way. In Paper Mario, Mario just sets the flower on the ground and it shoots fireballs at the enemies. If Mario Galaxy weren't here, it'd be easier to harmonize everything. Mario can either shoot fireballs directly out of the flower, or eat it to absorb the fire power (and possibly shoot the fireballs out of his mouth, the way it sort of looks in his SMB3 sprite and the way it was apparently designed to look for Luigi's sprite in the SMAS version of SMW.). Or you could just say that the clothes are representative of Mario holding the flower, and when he gets hit, it makes him drop the flower (like how powers were represented in SML2 with different hats because of technical limitations). However, the clothes showing up in Galaxy make the representation theory pretty hard to believe, and the time limit is inconsistent with all other games. But maybe only the terrestrial Fire Flowers last that long for some reason.
Mushrooms are definitely eaten, as seen most clearly in the Mario & Luigi games. The leaf is some kind of Tanooki magic that gets absorbed, but the Tanooki suit, like the Frog suit and Hammer suit, seems to just be an actual suit. The weird part is that the more naturalistic tanooki costume is the one that gives more tanooki powers. The P-Wing could just be an actual wing, and the designers just didn't have the time/space to make a separate sprite for it. The only clue for the feather I can find in the SMW manual is in the story at the beginning:
As they began their journey, Yoshi handed Mario a beautiful cape. "This may help you," Yoshi said. "Some say it has magical powers."
With a little luck (and help from a magic cape), our hearty crew can defeat the seven worlds of Bowser's Krazy Koopa Kritters.
So apparently the cape is magic. The fact that Yoshi gives Mario the cape, instead of a feather that turns into a cape, seems to indicate that the feather is representative, but since it's magic, it could just have the ability to change between forms at will.
Incidentally, I consider Smash to be at the same level of canon as the movie -- it's there if you want to pull anything neat out of it and adapt it, but everything else can be ignored.