Baking powder has a different texture than baking soda, and I think it is also more expensive. I quit baking years ago, so I haven't had to buy baking powder for a long time. I think baking soda also has some deoderizor properties because it can put in refrigerators as a deoderant. Also I have seen where people sprinkle it on carpeting and let it sit awhile, then vacume it up.
Baking powder is generally just baking soda mixed with an acid like cream of tartar. I'm sure it would work in a pinch but like redhatterb says plain baking soda would be cheaper to use. Borax and washing soda are often used as substitutes for baking soda in cleaning, but they are stronger and require special handling.
If you don't use much water you can scrub surfaces with salt. This works well on grease.