I also use the flushable/biodegradable diaper liners (Bummis makes some, and so does Imse Vimse (sp?); we like the Bummis better). You can buy the Bummis locally at Sprout Soup on High St in Columbus.
During any diaper change, if it's dirty, the liner goes into the toilet or port o'john, and the rest of the diaper goes into a zip loc bag. I sprinkle a little baking soda into the zip locs and pack a bunch like this, (sealed shut so the soda doesn't get everywhere).
If the liner is just wet, I flush it, or if that's not an option, I dispose of it in the trash. You can wash the liners (I have accidentally), but you can't reuse them since they sort of fall apart in the wash. (Bummis end up sort of like tangled yarn & get stuck in velcro but can be removed-be warned! LOL).
I keep the dirty diapers sealed up in the zip locs till I get a chance to wash, and then I usually do an extra rinse and wash cycle on top of my normal routine. I can fit 4 or 5 medium size dipes (for a 19m old) in a gallon ziploc.
Newborn/breastfed baby poop will pretty much just wash right out (in some cases, you might see some slight staining, but it's poop & that happens & is part of cloth diapering, imo. :) You can hang the diapers in the sun to help with staining if it bothers. I also do a cold wash, then a hot wash, to help prevent stains and get them really clean.