Mostly the essential oils can counteract the microbes as well as stress simultaneously but not all essential oils . main exceptions are bad odoured ones.
I think yes. Most of the essential oils have antibacterial properties and each type of essential oils might have antibacterial properties against specific strains of bacteria or other micro-organisms. For aromatherapy, essential oils obtained from selected aromatic plants like Bergamot, Citronella, Citrus, Chamomile, Tea tree, Geranium etc . are commonly used depending upon the condition of stress or other ailments. Although the same essential oil having both anti-microbial activity and stress relieving properties, however the mode of usage will be different.
I am not the subject matter expert on this specific topic but a friend of mine Atin Adhikari adhikari has done work. We coauthored a grant also to test the same hypothesis. The scientific evidence is that essential oils do have both properties.
I have come across some research studies showing that use of essential oils for cleaning of households and daycare centers effect kids mood positively.