Like a lot of my dried goods, I store oatmeal in mason jars using a vacuum sealer. Any FoodSaver or other brand of vacuum sealer that has an accessory port on it can be used with the mason jar attachment. You can get the mason jar attachment in regular or wide mouth. Sealing in a mason jar eliminates the need for oxygen absorbers, and allows you to safely store dried foods for many, many years.
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FoodSaver FM2000 Vacuum Sealer Machine
https://amzn.to/2uGdlmY
Regular-Mouth Jar Attachment
https://amzn.to/2HUKfIY
Wide-Mouth Jar Attachment
https://amzn.to/2WMipCr