I'm not an expert, over and above what I know from selling and using oils for many years. The concentration of oil in the air from any dispersal method I can think of is likely to be insufficient to affect viruses and mould in the air. You would need such a strength, I believe, that the odour and effect on people and pets could be prohibitive.
With anti viral oils (tea tree for example) I would say you must inhale the vapour - from the oil being in hot water for example - to attack a virus such as the common cold. Some oils, where acceptable for direct skin contact, will kill germs, etc., and aid healing.
Lavender in a room burner or diffuser can be very effective at calming and aiding sleep. Used directly on the skin it will aid healing, especially on burns.
I would be interested to know if oils can be used in the way you describe nohorn, but I think your mould spores need addressing by another method and possibly more ventilation in your kitchen.