Oversampling a signal
From that same page you link to:


  A signal is said to be oversampled by a factor of N if it is sampled at N times the Nyquist rate. 


So, you're sampling at $1\cdot10^4\,\text{Hz}$, that's $N=\frac{10^4}{140}\approx 71$; no need to subtract anything.


  Does this oversampling only reduce the noise introduced from the output of the analogue sensor (given the low bandwidth of the sensor) to the end of the ADC process?


Oversampling alone doesn't reduce noise. It's what you do afterwards with the signal. Oversampling can be necessary to e.g. to be able to filter out the noise that can be shaped to your advantage.


  How much can I reduce the oversampling (which introduces a processor overhead) by for a negligible increase in the amount of noise to the signal?


You need to define "negligible"; also, you need to think about the noise is distributed in frequency domain during your sampling process; there's no general answer.


  Could I do anything else to reduce the amount of oversampling, e.g increase the ADC resolution?


I'm confused: The only way to reduce oversampling is to reduce the sampling rate.

Maybe you mean


  to reduce the necessary amount of oversampling


Well, that fully depends on your signal, and what you want to do with it, and you forgot to tell us about either!