Guitar stinks. Can I just re-oil the fretboard?

I sent my guitar to the luthier and whatever they applied on the guitar made the neck stink sweat so much to the point I'm unconsciously avoiding playing the guitar.

Last time I changed the string, I used Johnson & Johnson baby oil since I didn't have any other kind of oil and the guitar had a very pleasant smell to it.

Now I would like to remove this oil the luthier used and apply J&J oil. I have two questions though:

1 - do I need to remove the "old" oil before applying the new one or can I just slap on top of it and call it a day?

2 - do I need to remove the brand new strings to repply the oil or can I just put oil with them on and it'll be fine - and call it a day - ?

Honestly I'm not even sure if the oil is the culprit, although it seems so, as I don't smell any stink in the bridge/pups area, nor around the headstock and I'm assuming it's the fretboard.

Lastly: sorry if this is a dumb question, it's my first guitar and I don't know much about taking care of it so what it might seems obvious to you it is not for me. But I trully appreciate your help in this matter :)