I do this but with conditioner in my hair, not oils. I just call it an overnight baggy treatment.
I wash my hair in the night and when it is just damp I apply a conditioner on may hair, not my scalp. Then I put a shower cap over it and a beanie hat over the shower cap. Then I go to bed.
The next morning I remove the hat and the shower cap and either rinse off the conditioner or leave it in (depending on the conditioner) and let my hair air-dry.
This treatment seems to infuse moisture in my hair and scalp however, it is a real pain to do, sleeping with all that paraphernalia on your head, and the husband does not appreciate it either, LOL.