Recipe: Flavored Oils (re: dried tomatoes in oil)

I am sorry, but you will not be able to can them in oil.
You can store them if really dried and crispy in oil in the fridge for a short time.
You can also freeze it.

FLAVORED OILS

Infused oils and oil-based mixtures of garlic, herbs or dried tomatoes can pose a health hazard if not kept refrigerated. There have been a number of cases of botulism poisoning traced to commercially and home prepared mixtures of garlic-in-oil that were not refrigerated. Refrigeration is necessary because all other conditions that favor the growth of C. botulinum are met: low acid environment with pH higher that 4.6, anaerobic conditions (oil), food and moisture source (garlic), not boiled before eating. Vegetables and herbs in oil. Less has been documented on the dangers of storing whole chilies, fleshy vegetables or herbs in oil, but they, too, are best made fresh with leftovers stored in the refrigerator for use within three weeks. Vegetables have a high water activity level which further encourages the growth of C. botulinum bacteria in an anaerobic environment.

Even when dried, there is still the potential for risk, unless the vegetable has been acidified to a pH of 4.6 or lower. Dried tomatoes in oil are less of a safety concern than other mixtures in oil because the pH of tomatoes is generally 4.6 or lower. In addition, by drying the tomatoes, conditions become even less favorable to growth of C. botulinum due to a decrease in water activity. Dried herbs in oil also are less of a safety concern because of their low water activity. However, to insure safety it is recommended that all tomato in oil and herb in oil products be stored at refrigerator temperatures.

Avoid Rancidity
In addition to reducing the potential for growth of C. botulinum bacteria, storing flavored oils in the refrigerator helps keep the oils from becoming rancid. A putrid "off" odor indicates the development of rancidity. All fats and oils will become rancid given enough exposure to air, sunlight and heat. Polyunsaturated fats, like vegetable oils, are especially prone to such deterioration. Eating rancid food won't make you sick, but it may be unhealthy in the long run. Rancid fat contains chemicals called peroxides and aldehydes that can damage cells and may even encourage cholesterol to clog arteries.

It is important to note that rancidity and the presence of botulinal toxins are not necessarily related. Toxin may be present without any hint of an off-odor. Likewise, an off-odor does not necessarily indicate the presence of botulism toxin. It does, however, indicate the product may have been left for long periods at room temperature, which would promote the growth of C. botulinum. Therefore, it's best to discard any oil-based mixtures that have become rancid so they're out of reach of humans or animals.