Don, even if you put too much oil on each of the the spoke/nipple joints it is unlikely to get anywhere near the inner tube.
As soon as you start riding, the centrifugal force will soon fling off any excess oil externally, but it may affect your rear brake if you don't have disc brakes and some of the oil ends up on the braking portion of the rim.
I find that tyres tend to be quite resistant to oil, as when I lube my chain, the excess oil always ends up on the sidewall of the rear tyre, but I've never had to replace a tyre due to the effects of oil.
They are usually replaced because the tread has completely worn out or because they have been severely damaged by riding over a sharp object.
Alan