Alright so i was trying to remove my lenovo T61 heatsink and there was a very stuck screw that didn't want to come off (and it didn't) so i put a very small drop of oil using a needle, on the screw to loosen it a bit i'm afraid that it will get to the motherboard and damage something.
The thing circled in red and black is the screw i spilled a droplet of oil on it: 
This shouldn't really affect much, just clean it up with 100% alcohol if its on your motherboard or CPU.
Oil is thick, so it will take its time or not bother going through tight spots. When unscrewing this screw, I would place a tissue or a cloth to clear up the oil when loosening.
No, it won't effect much. Clean it properly by using cleaner or Colin. Don't use water it may damage your device.
I saw an article the other day about this, let me check my history real fast and I will get back with the link