The two main reasons for oiling leather are preservation and to increase it's water resistance.
The fibers in leather can break down over time...a process which is accelerated by heat and humidity (both high and low). Oiling keeps the leather supple and works to prevent the fiber breakdown.
Most strops come from the manufacturer ready to use and under normal heat/humidity conditions probably only need a very light application of oil once or at most twice a year.
If your new strop is very stiff and looks and feels dry then by all means oil it...but don't go overboard. I'm partial to Lexol products...they make a great cleaner and a conditioner that are inexpensive, are specifically formulated for leather, and if you follow the directions it's pretty hard to overdo it.