Most likely not oil but old fat and grease from the previous owner. deep fat fryer the most likely cause as the fat will turn to liquid when heated by steam from your cooking etc etc. Change the filters or stick them in the dishwasher if the newer type.
Def clean it, plenty of hot soapy water in your sink but squeeze out your cloth. Every cookerhood is different so just remember how you took it "apart" as in my first job on a summer cleanup somehow I just took out the two panels underneath the cookerhood and for the life of me couldn't manage to get them back up. Eventually did.
I'd imagine that if it is so clogged up, it is not working properly. Certainly a major clean and overhaul, if not a skip job. New ones are relatively cheap. And installation is pretty simple - normally.