I would not worry about using the Oil rule in either intro scenario, as they are so short. Oil use has long-term strategic implications.
I would suggest just using the optional rules for Offensive Chits, Artillery, Fortifications, Siberians, and Off-City Reinforcements. The last three are extremely simple ones. I would even start without adding Divisions to keep counter density real low and help illustrate combat loss potential.
Overruns require 7:1 odds and an ARM or MECH unit in the stack doing the overrun, can only be done in clear terrain, and costs the overrunning units an extra movement point.
Units that are out of supply defend at reduced strength of 1 if “disorganized” or 3 if “disorganized” and “elite.” “Elite” units have white combat factors shown. Units become “disorganized” a variety of ways - after a successful enemy Ground Strike mission, after a retreat result in combat, after moving when they started out of supply, or if they enter a hex which requires more movement points than they have left, which is legal but disorganization is the penalty.
In the Barbarossa scenario there are only a few weak Russian units that can be straight overrun when they are in-supply and not disorganized, and that requires a German stack of their 2 best Panzer units. However as the scenario moves along other overrun potential situations may occur.
Also note that playing an Offensive Chit can allow a temporary doubling of the combat factors of a limited number of units in ‘range’ of a designated HQ unit. These doublings can be used during the movement phase to conduct an overrun.
Note that defending unit combat factors are calculated at the moment of dice rolling each individual combat - not at the moment all attacks are declared simultaneously, though that would be after land movement which is usually when overrun occurs.