I have a few expensive guitars and I've never oiled them once. When I change my strings, I use some lemon or orange Pledge to wipe the fretboard down and that is it.
As far as tuning with a Floyd Rose, I adjust the springs every time, as well as move the fine tuners back into the middle position. I actually dislike the Floyd Rose, but I'm not a whammy bar kinda guy.
I have an acoustic guitar I bought maybe 10 years ago. Never oiled it once, never changed the strings. Changed the strings about 2 weeks ago and oiled the fretboard. It needed it. Plays better now and the fretboard looks better than it did.
I have my Dad's Gibson SG, he has owned this guitar since the 1980s (it is a 1978 IIRC) but it hasn't been played in probably 10 years (my Dad passed away 5 years ago and he was suffering from medical issues for a few years prior to his passing). Anyway, the guitar needed strings badly and it also needed a good cleaning. One of the pickups had some build up on it but once I cleaned it and changed the strings it plays soo sweet now. Really a nice sounding guitar.
I have a '95 Fender Jag-Stang my Dad owned too. It is a left-handed guitar and it is in mint condition. I figured my son could play it. Guitar had the original strings on it and they wouldn't hold a tune for very long and they were really quite old. I put new strings on it and oiled the fretboard and it sounds much better (I can't play it though... damned lefties).
I would recommend oiling the fretboard when changing strings, especially if you live in a dry climate like I do. Use something made specifically for guitars though.