How to store oatmeal
Best place: the pantry. Oatmeal is shelf stable and keeps for 12 months in a cool, dry cupboard, then 6 to 12 months once opened.

Where these times come from. USDA FoodKeeper has no entry named "oatmeal". The 2 kinds on this page are the USDA entries that cover oatmeal, copied without change from Cereal and Oats. Each row in the table is one USDA entry; pick the one that matches what you have.
12 months
from the package date
No guideline
No guideline
How to tell oatmeal has gone bad
General signs for shelf stable foods, the group USDA lists oatmeal under.
- Crackers or cereal that have gone soft or stale, not crisp
- Rancid, paint-like smell from nuts, oils or nut butters
- Small insects or webbing inside a box or bag
- Spices that have lost their smell and colour
- Fermented or boozy smell from honey that has picked up moisture
More on shelf stable foods. The times above are quality guidelines, not safety limits; food that shows these signs goes out regardless of the date.
Storage habits that make the difference
Store dry pantry staples in a cool, dry cupboard away from the stove and direct sunlight, ideally in airtight containers once opened. Reseal cracker and cereal bags tightly with a clip or transfer them to a container to keep them crisp. Label opened jars with the date so older ones get used first.
How to store other shelf stable foods
Source: USDA FSIS FoodKeeper dataset (public domain). How we decode the data.