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The self-cleaning oven turns spills in the oven into ash that is easy to get out. The trade-off is that the process produces smoke that can get all over your house. The smoke can get in your soft goods (padded furniture, draperies) so it may take a few days to completely dissipate. A bit of air sanitizer spray such as Oust will help with the odor, as will providing as much fresh air exchange as possible in the winter.
The only reported danger from self-cleaning ovens is to birds who have extremely sensitive respiratory systems. Some self-cleaning ovens contain PTFE which can produce fumes that are toxic to birds. Common sense would dictate that persons with respiratory problems also be away from home during the self-cleaning and airing cycle.