I've not heard of using it for a respiratory issue. But, do you have the instructions as to how to go about it? An essential oil is generally diluted with another liquid - water or another oil (i.e. olive oil). I would be cautious just applying it to the bird with no instructions.
Vetrx would be used just to allow the birds nasal passages to open up - like you would with vicks vapor rub for a person. It's not going to cure them though.
But, I have read a drop of oregano oil per gallon of water is safe for them if that's your intention.
Do you have a dropper? Are you familiar with using essential oils?