I use Nalgene's polyethylene screw-top containers. They're both water- and air-proof. They come in all sizes, so you can use different ones for different trip lengths. You just need to remember which pills to take in the morning, and which at night. Or, you could take an "AM" bottle and a "PM" bottle. Heck, some of those bottles are so small that you could use a different one for each med. At home, I store my meds and vitamins in 2 oz. bottles, which hold over a month's worth of vitamin-sized pills.
My pharma buddy thinks most pills will have an effective shelf life of about a year, providing you keep them away from the demons of heat, moisture, and direct sunlight.
(edited for shelf life comment)