Converting 8/3 220VAC oven recptacle to 120V recptacle
Retrofitting ground to a range circuit

As of 2014, Code greatly broadened the rules for retrofitting ground wires.  If it was simply a matter of provisioning a ground wire to that range circuit, there would be no problem at all. 

A 40A circuit requires a #10 ground wire, green or bare. You can always use a larger wire.  It only needs to follow the rules for routing and protecting ground wires, and it can follow any route back to the service panel.  It doesn't need to go to the panel, only to 


any outlet or junction which also has a #10 or larger ground going back to the panel (water heater, A/C, dryer if grounded, etc. 
anywhere on the grounding electrode system (the wire to your ground rods) I do not endorse using a general water pipe, because further plumbing mods may separate that. 
any junction box connected by all metal conduit back to the panel. 


At that point you convert the range receptacle to NEMA 14-50 and change the range plug and jumper, done.  

If you were to do this before you converted the circuit to 120V/20A use, there's no question it's legit. 

Retrofitting ground to a brand new 20A circuit

This is more fuzzy and I just don't know for sure.  I fear it may be subject to interpretation by AHJ.   I am concerned that if you had a 3-wire range connection, and then you converted it to 20A receptacles, and then you grounded it, the ruling might be "this is new work; the retrofit rules don't apply to new work; run new homerun(s).” 

However if the AHJ is simpatico with this application, then you would be able to retrofit ground to these new receptacle circuits.  Same rules as above, however, the size of ground wire you need is 12 AWG (14 AWG if 15A circuit).  Obviously this is a lot easier, because you only need to reach a point with a #12 (or #14) ground wire running back to the panel, and that can probably be found a whole lot closer. 

And to be clear on this point, larger wire than proscribed is always OK.  Suppose the required size is #12... you use #8 ground wire because you have some. You reach a point with #10 running back to the panel. That's all fine for grounding either a 40A or 15/20A circuit.