If it was truely airtight, the smell molecules would remain inside the box. However, even objects branded as airtight in this day and age usually isn't airtight, especially if it can be opened (it's not like the space between the lid and the box isn't going to be less than an air molecule thick at all points around the lid, is it?). If this is the case then the smell will indeed gradually escape.
Also, some plastics are pourous, meaning they gradually let air seep through them over very long periods of time.
Regarding the water in the jar - the same applies here: the space between the lid and the jar must be less than the space taken up by an air molecule or else the water cannot escape. Therefore if the water doesn't escape, it will have evapourated into the air. However, the water will not disappear if there is enough in the jar, because eventually the air will be saturated and no more water will be allowed to evapourate.