I have triplet boys (almost 22 mos)! I hope you're feeling okay with being pregnant again. I think I would have gone insane if I had gotten pregnant again so soon.
I haven't had any problems with stinky sippy cups (unless they get left in the car for a week), because as soon as my boys are done drinking I rinse them out then wash them at the end of the day (we have 2 or 3 per boy). I also don't let them tug them around the house so they are laying around for hours without me knowing where they are. I only let them drink in their high chairs or sitting at the table.
You may just want to buy some new ones and then make sure to round them up within an hour or so of handing them out to rinse or wash right then and there.