Oligos in their dry state are stable for several months and should undergo no measurable degradation during their time in transit, even in the case of delays. Resuspended oligos are less stable than those left dry, however.
Oligos stored dry, or in non-DEPC treated water for that matter, are very stable for the short period of time it takes to ship an oligo. IDT ships its oligos dry to provide the researcher complete control over the reagents they want to use for resuspension. (Any oligo that could potentially degrade while in transit will be shipped frozen.)
For long term storage, temperature is the most important factor to consider. For long term storage, whether oligos are dried down, or resuspended in water (non-DEPC treated) or TE Buffer (10 mM Tris pH 8.0, 0.1 mM EDTA; such as IDTE), it is optimal to store them frozen at -20°C. For room temperature or 4°C storage, oligos that are resuspended in TE buffer are more stable than dry oligos. Oligos that are stored in water are the least stable. However, at 4°C oligos stored under all of these conditions are stable for at least 60 weeks.
Please see the Technical Report, Oligonucleotide Stability Study for data on oligonucleotide storage and a more thorough explanation.